---
_id: '8682'
abstract:
- lang: eng
text: It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous
for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover,
for such varieties it follows from a general conjecture of Colliot-Thélène that
the Brauer--Manin obstruction to the Hasse principle should be the only one, so
that the Hasse principle is expected to hold. Working over the field of rational
numbers and ordering Fano hypersurfaces of fixed degree and dimension by height,
we prove that almost every such hypersurface satisfies the Hasse principle provided
that the dimension is at least 3. This proves a conjecture of Poonen and Voloch
in every case except for cubic surfaces.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Pierre Le
full_name: Boudec, Pierre Le
last_name: Boudec
- first_name: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces.
Annals of Mathematics. 2023;197(3):1115-1203. doi:10.4007/annals.2023.197.3.3
apa: Browning, T. D., Boudec, P. L., & Sawin, W. (2023). The Hasse principle
for random Fano hypersurfaces. Annals of Mathematics. Princeton University.
https://doi.org/10.4007/annals.2023.197.3.3
chicago: Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle
for Random Fano Hypersurfaces.” Annals of Mathematics. Princeton University,
2023. https://doi.org/10.4007/annals.2023.197.3.3.
ieee: T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random
Fano hypersurfaces,” Annals of Mathematics, vol. 197, no. 3. Princeton
University, pp. 1115–1203, 2023.
ista: Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano
hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.
mla: Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.”
Annals of Mathematics, vol. 197, no. 3, Princeton University, 2023, pp.
1115–203, doi:10.4007/annals.2023.197.3.3.
short: T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.
date_created: 2020-10-19T14:28:50Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-08-11T11:59:49Z
day: '01'
department:
- _id: TiBr
doi: 10.4007/annals.2023.197.3.3
external_id:
arxiv:
- '2006.02356'
isi:
- '000966611000003'
oaworkID:
- w3033938593
intvolume: ' 197'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2006.02356
month: '05'
oa: 1
oa_version: Preprint
oaworkID: 1
page: 1115-1203
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Princeton University
quality_controlled: '1'
related_material:
link:
- description: News on IST Homepage
relation: press_release
url: https://ist.ac.at/en/news/when-is-necessary-sufficient/
status: public
title: The Hasse principle for random Fano hypersurfaces
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 197
year: '2023'
...
---
_id: '13091'
abstract:
- lang: eng
text: We use a function field version of the Hardy–Littlewood circle method to study
the locus of free rational curves on an arbitrary smooth projective hypersurface
of sufficiently low degree. On the one hand this allows us to bound the dimension
of the singular locus of the moduli space of rational curves on such hypersurfaces
and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin
conjecture in terms of slopes with respect to the tangent bundle.
acknowledgement: The authors are grateful to Paul Nelson, Per Salberger and Jason
Starr for useful comments. While working on this paper the first author was supported
by EPRSC grant EP/P026710/1. The research was partially conducted during the period
the second author served as a Clay Research Fellow, and partially conducted during
the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and
the ETH Zurich Foundation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and
the circle method. Algebra and Number Theory. 2023;17(3):719-748. doi:10.2140/ant.2023.17.719
apa: Browning, T. D., & Sawin, W. (2023). Free rational curves on low degree
hypersurfaces and the circle method. Algebra and Number Theory. Mathematical
Sciences Publishers. https://doi.org/10.2140/ant.2023.17.719
chicago: Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree
Hypersurfaces and the Circle Method.” Algebra and Number Theory. Mathematical
Sciences Publishers, 2023. https://doi.org/10.2140/ant.2023.17.719.
ieee: T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces
and the circle method,” Algebra and Number Theory, vol. 17, no. 3. Mathematical
Sciences Publishers, pp. 719–748, 2023.
ista: Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces
and the circle method. Algebra and Number Theory. 17(3), 719–748.
mla: Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces
and the Circle Method.” Algebra and Number Theory, vol. 17, no. 3, Mathematical
Sciences Publishers, 2023, pp. 719–48, doi:10.2140/ant.2023.17.719.
short: T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748.
date_created: 2023-05-28T22:01:02Z
date_published: 2023-04-12T00:00:00Z
date_updated: 2023-08-01T14:51:57Z
day: '12'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/ant.2023.17.719
external_id:
arxiv:
- '1810.06882'
isi:
- '000996014700004'
file:
- access_level: open_access
checksum: 5d5d67b235905650e33cf7065d7583b4
content_type: application/pdf
creator: dernst
date_created: 2023-05-30T08:05:22Z
date_updated: 2023-05-30T08:05:22Z
file_id: '13101'
file_name: 2023_AlgebraNumberTheory_Browning.pdf
file_size: 1430719
relation: main_file
success: 1
file_date_updated: 2023-05-30T08:05:22Z
has_accepted_license: '1'
intvolume: ' 17'
isi: 1
issue: '3'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 719-748
project:
- _id: 26A8D266-B435-11E9-9278-68D0E5697425
grant_number: EP-P026710-2
name: Between rational and integral points
publication: Algebra and Number Theory
publication_identifier:
eissn:
- 1944-7833
issn:
- 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free rational curves on low degree hypersurfaces and the circle method
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 17
year: '2023'
...
---
_id: '13180'
abstract:
- lang: eng
text: We study the density of everywhere locally soluble diagonal quadric surfaces,
parameterised by rational points that lie on a split quadric surface
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Julian
full_name: Lyczak, Julian
id: 3572849A-F248-11E8-B48F-1D18A9856A87
last_name: Lyczak
- first_name: Roman
full_name: Sarapin, Roman
last_name: Sarapin
citation:
ama: Browning TD, Lyczak J, Sarapin R. Local solubility for a family of quadrics
over a split quadric surface. Involve. 2023;16(2):331-342. doi:10.2140/involve.2023.16.331
apa: Browning, T. D., Lyczak, J., & Sarapin, R. (2023). Local solubility for
a family of quadrics over a split quadric surface. Involve. Mathematical
Sciences Publishers. https://doi.org/10.2140/involve.2023.16.331
chicago: Browning, Timothy D, Julian Lyczak, and Roman Sarapin. “Local Solubility
for a Family of Quadrics over a Split Quadric Surface.” Involve. Mathematical
Sciences Publishers, 2023. https://doi.org/10.2140/involve.2023.16.331.
ieee: T. D. Browning, J. Lyczak, and R. Sarapin, “Local solubility for a family
of quadrics over a split quadric surface,” Involve, vol. 16, no. 2. Mathematical
Sciences Publishers, pp. 331–342, 2023.
ista: Browning TD, Lyczak J, Sarapin R. 2023. Local solubility for a family of quadrics
over a split quadric surface. Involve. 16(2), 331–342.
mla: Browning, Timothy D., et al. “Local Solubility for a Family of Quadrics over
a Split Quadric Surface.” Involve, vol. 16, no. 2, Mathematical Sciences
Publishers, 2023, pp. 331–42, doi:10.2140/involve.2023.16.331.
short: T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 331–342.
date_created: 2023-07-02T22:00:43Z
date_published: 2023-05-26T00:00:00Z
date_updated: 2023-07-17T08:39:19Z
day: '26'
department:
- _id: TiBr
doi: 10.2140/involve.2023.16.331
external_id:
arxiv:
- '2203.06881'
intvolume: ' 16'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2203.06881
month: '05'
oa: 1
oa_version: Preprint
page: 331-342
publication: Involve
publication_identifier:
eissn:
- 1944-4184
issn:
- 1944-4176
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local solubility for a family of quadrics over a split quadric surface
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 16
year: '2023'
...
---
_id: '12916'
abstract:
- lang: eng
text: "We apply a variant of the square-sieve to produce an upper bound for the
number of rational points of bounded height on a family of surfaces that admit
a fibration over P1 whose general fibre is a hyperelliptic curve. The implied
constant does not depend on the coefficients of the polynomial defining the surface.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dante
full_name: Bonolis, Dante
id: 6A459894-5FDD-11E9-AF35-BB24E6697425
last_name: Bonolis
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic
fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze.
2023;24(1):173-204. doi:10.2422/2036-2145.202010_018
apa: Bonolis, D., & Browning, T. D. (2023). Uniform bounds for rational points
on hyperelliptic fibrations. Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale. https://doi.org/10.2422/2036-2145.202010_018
chicago: Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points
on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale, 2023.
https://doi.org/10.2422/2036-2145.202010_018.
ieee: D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic
fibrations,” Annali della Scuola Normale Superiore di Pisa - Classe di Scienze,
vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204,
2023.
ista: Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic
fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze.
24(1), 173–204.
mla: Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points
on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della
Normale, 2023, pp. 173–204, doi:10.2422/2036-2145.202010_018.
short: D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa
- Classe Di Scienze 24 (2023) 173–204.
date_created: 2023-05-07T22:01:04Z
date_published: 2023-02-16T00:00:00Z
date_updated: 2023-10-18T06:54:30Z
day: '16'
department:
- _id: TiBr
doi: 10.2422/2036-2145.202010_018
external_id:
arxiv:
- '2007.14182'
intvolume: ' 24'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2007.14182
month: '02'
oa: 1
oa_version: Preprint
page: 173-204
publication: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
publication_identifier:
eissn:
- 2036-2145
issn:
- 0391-173X
publication_status: published
publisher: Scuola Normale Superiore - Edizioni della Normale
quality_controlled: '1'
scopus_import: '1'
status: public
title: Uniform bounds for rational points on hyperelliptic fibrations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '9199'
abstract:
- lang: eng
text: "We associate a certain tensor product lattice to any primitive integer lattice
and ask about its typical shape. These lattices are related to the tangent bundle
of Grassmannians and their study is motivated by Peyre's programme on \"freeness\"
for rational points of bounded height on Fano\r\nvarieties."
acknowledgement: The authors are very grateful to Will Sawin for useful remarks about
this topic. While working on this paper the first two authors were supported by
EPSRC grant EP/P026710/1, and the first and last authors by FWF grant P 32428-N35.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Tal
full_name: Horesh, Tal
id: C8B7BF48-8D81-11E9-BCA9-F536E6697425
last_name: Horesh
- first_name: Florian Alexander
full_name: Wilsch, Florian Alexander
id: 560601DA-8D36-11E9-A136-7AC1E5697425
last_name: Wilsch
orcid: 0000-0001-7302-8256
citation:
ama: Browning TD, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians.
Algebra & Number Theory. 2022;16(10):2385-2407. doi:10.2140/ant.2022.16.2385
apa: Browning, T. D., Horesh, T., & Wilsch, F. A. (2022). Equidistribution and
freeness on Grassmannians. Algebra & Number Theory. Mathematical Sciences
Publishers. https://doi.org/10.2140/ant.2022.16.2385
chicago: Browning, Timothy D, Tal Horesh, and Florian Alexander Wilsch. “Equidistribution
and Freeness on Grassmannians.” Algebra & Number Theory. Mathematical
Sciences Publishers, 2022. https://doi.org/10.2140/ant.2022.16.2385.
ieee: T. D. Browning, T. Horesh, and F. A. Wilsch, “Equidistribution and freeness
on Grassmannians,” Algebra & Number Theory, vol. 16, no. 10. Mathematical
Sciences Publishers, pp. 2385–2407, 2022.
ista: Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians.
Algebra & Number Theory. 16(10), 2385–2407.
mla: Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.”
Algebra & Number Theory, vol. 16, no. 10, Mathematical Sciences Publishers,
2022, pp. 2385–407, doi:10.2140/ant.2022.16.2385.
short: T.D. Browning, T. Horesh, F.A. Wilsch, Algebra & Number Theory 16 (2022)
2385–2407.
date_created: 2021-02-25T09:56:57Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-02T06:46:38Z
day: '01'
department:
- _id: TiBr
doi: 10.2140/ant.2022.16.2385
external_id:
arxiv:
- '2102.11552'
isi:
- '000961514100004'
intvolume: ' 16'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2102.11552
month: '12'
oa: 1
oa_version: Preprint
page: 2385-2407
project:
- _id: 26A8D266-B435-11E9-9278-68D0E5697425
grant_number: EP-P026710-2
name: Between rational and integral points
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Algebra & Number Theory
publication_identifier:
eissn:
- 1944-7833
issn:
- 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equidistribution and freeness on Grassmannians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 16
year: '2022'
...
---
_id: '12776'
abstract:
- lang: eng
text: An improved asymptotic formula is established for the number of rational points
of bounded height on the split smooth del Pezzo surface of degree 5. The proof
uses the five conic bundle structures on the surface.
acknowledgement: This work was begun while the author was participating in the programme
on "Diophantine equations" at the Hausdorff Research Institute for Mathematics in
Bonn in 2009. The hospitality and financial support of the institute is gratefully
acknowledged. The idea of using conic bundles to study the split del Pezzo surface
of degree 5 was explained to the author by Professor Salberger. The author is very
grateful to him for his input into this project and also to Shuntaro Yamagishi for
many useful comments on an earlier version of this manuscript. While working on
this paper the author was supported by FWF grant P32428-N35.
article_processing_charge: No
article_type: original
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo
surface of degree 5. New York Journal of Mathematics. 2022;28:1193-1229.
apa: Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split
del Pezzo surface of degree 5. New York Journal of Mathematics. State University
of New York.
chicago: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split
Del Pezzo Surface of Degree 5.” New York Journal of Mathematics. State
University of New York, 2022.
ieee: T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo
surface of degree 5,” New York Journal of Mathematics, vol. 28. State University
of New York, pp. 1193–1229, 2022.
ista: Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del
Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.
mla: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del
Pezzo Surface of Degree 5.” New York Journal of Mathematics, vol. 28, State
University of New York, 2022, pp. 1193–229.
short: T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.
date_created: 2023-03-28T09:21:09Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2023-10-18T07:59:13Z
day: '24'
ddc:
- '510'
department:
- _id: TiBr
file:
- access_level: open_access
checksum: c01e8291794a1bdb7416aa103cb68ef8
content_type: application/pdf
creator: dernst
date_created: 2023-03-30T07:09:35Z
date_updated: 2023-03-30T07:09:35Z
file_id: '12778'
file_name: 2022_NYJM_Browning.pdf
file_size: 897267
relation: main_file
success: 1
file_date_updated: 2023-03-30T07:09:35Z
has_accepted_license: '1'
intvolume: ' 28'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 1193 - 1229
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: New York Journal of Mathematics
publication_identifier:
issn:
- 1076-9803
publication_status: published
publisher: State University of New York
quality_controlled: '1'
status: public
title: Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree
5
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2022'
...
---
_id: '8742'
abstract:
- lang: eng
text: We develop a version of Ekedahl’s geometric sieve for integral quadratic forms
of rank at least five. As one ranges over the zeros of such quadratic forms, we
use the sieve to compute the density of coprime values of polynomials, and furthermore,
to address a question about local solubility in families of varieties parameterised
by the zeros.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath-Brown
citation:
ama: Browning TD, Heath-Brown R. The geometric sieve for quadrics. Forum Mathematicum.
2021;33(1):147-165. doi:10.1515/forum-2020-0074
apa: Browning, T. D., & Heath-Brown, R. (2021). The geometric sieve for quadrics.
Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2020-0074
chicago: Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.”
Forum Mathematicum. De Gruyter, 2021. https://doi.org/10.1515/forum-2020-0074.
ieee: T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” Forum
Mathematicum, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021.
ista: Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum
Mathematicum. 33(1), 147–165.
mla: Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.”
Forum Mathematicum, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:10.1515/forum-2020-0074.
short: T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165.
date_created: 2020-11-08T23:01:25Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-10-17T07:39:01Z
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- '2003.09593'
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project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Forum Mathematicum
publication_identifier:
eissn:
- 1435-5337
issn:
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publisher: De Gruyter
quality_controlled: '1'
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title: The geometric sieve for quadrics
type: journal_article
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volume: 33
year: '2021'
...
---
_id: '9260'
abstract:
- lang: eng
text: We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ)
when Δ is a Q-divisor involving hyperplanes. This allows us to address a question
of Tanimoto about whether the set of rational points on such an orbifold constitutes
a thin set. Our approach relies on the Hardy–Littlewood circle method to first
study an asymptotic version of Waring’s problem for mixed powers. In doing so
we make crucial use of the recent resolution of the main conjecture in Vinogradov’s
mean value theorem, due to Bourgain–Demeter–Guth and Wooley.
acknowledgement: While working on this paper the authors were both supported by EPSRC
grant EP/P026710/1, and the second author received additional support from the NWO
Veni Grant 016.Veni.192.047. Thanks are due to Marta Pieropan, Arne Smeets and Sho
Tanimoto for useful conversations related to this topic, and to the anonymous referee
for numerous helpful suggestions.
article_processing_charge: No
article_type: original
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Shuntaro
full_name: Yamagishi, Shuntaro
last_name: Yamagishi
citation:
ama: Browning TD, Yamagishi S. Arithmetic of higher-dimensional orbifolds and a
mixed Waring problem. Mathematische Zeitschrift. 2021;299:1071–1101. doi:10.1007/s00209-021-02695-w
apa: Browning, T. D., & Yamagishi, S. (2021). Arithmetic of higher-dimensional
orbifolds and a mixed Waring problem. Mathematische Zeitschrift. Springer
Nature. https://doi.org/10.1007/s00209-021-02695-w
chicago: Browning, Timothy D, and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional
Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift. Springer
Nature, 2021. https://doi.org/10.1007/s00209-021-02695-w.
ieee: T. D. Browning and S. Yamagishi, “Arithmetic of higher-dimensional orbifolds
and a mixed Waring problem,” Mathematische Zeitschrift, vol. 299. Springer
Nature, pp. 1071–1101, 2021.
ista: Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds
and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101.
mla: Browning, Timothy D., and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional
Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift, vol.
299, Springer Nature, 2021, pp. 1071–1101, doi:10.1007/s00209-021-02695-w.
short: T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 1071–1101.
date_created: 2021-03-21T23:01:21Z
date_published: 2021-03-05T00:00:00Z
date_updated: 2023-08-07T14:20:00Z
day: '05'
ddc:
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department:
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doi: 10.1007/s00209-021-02695-w
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grant_number: EP-P026710-2
name: Between rational and integral points
publication: Mathematische Zeitschrift
publication_identifier:
eissn:
- 1432-1823
issn:
- 0025-5874
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic of higher-dimensional orbifolds and a mixed Waring problem
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...
---
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abstract:
- lang: eng
text: The Hardy–Littlewood circle method was invented over a century ago to study
integer solutions to special Diophantine equations, but it has since proven to
be one of the most successful all-purpose tools available to number theorists.
Not only is it capable of handling remarkably general systems of polynomial equations
defined over arbitrary global fields, but it can also shed light on the space
of rational curves that lie on algebraic varieties. This book, in which the arithmetic
of cubic polynomials takes centre stage, is aimed at bringing beginning graduate
students into contact with some of the many facets of the circle method, both
classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i
Balaguer Prize, a prestigious award for books of expository nature presenting
the latest developments in an active area of research in mathematics.
alternative_title:
- Progress in Mathematics
article_processing_charge: No
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: 'Browning TD. Cubic Forms and the Circle Method. Vol 343. Cham: Springer
Nature; 2021. doi:10.1007/978-3-030-86872-7'
apa: 'Browning, T. D. (2021). Cubic Forms and the Circle Method (Vol. 343).
Cham: Springer Nature. https://doi.org/10.1007/978-3-030-86872-7'
chicago: 'Browning, Timothy D. Cubic Forms and the Circle Method. Vol. 343.
Cham: Springer Nature, 2021. https://doi.org/10.1007/978-3-030-86872-7.'
ieee: 'T. D. Browning, Cubic Forms and the Circle Method, vol. 343. Cham:
Springer Nature, 2021.'
ista: 'Browning TD. 2021. Cubic Forms and the Circle Method, Cham: Springer Nature,
XIV, 166p.'
mla: Browning, Timothy D. Cubic Forms and the Circle Method. Vol. 343, Springer
Nature, 2021, doi:10.1007/978-3-030-86872-7.
short: T.D. Browning, Cubic Forms and the Circle Method, Springer Nature, Cham,
2021.
date_created: 2021-12-05T23:01:46Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2022-06-03T07:38:33Z
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department:
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doi: 10.1007/978-3-030-86872-7
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title: Cubic Forms and the Circle Method
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volume: 343
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...
---
_id: '177'
abstract:
- lang: eng
text: We develop a geometric version of the circle method and use it to compute
the compactly supported cohomology of the space of rational curves through a point
on a smooth affine hypersurface of sufficiently low degree.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Sawin W. A geometric version of the circle method. Annals of
Mathematics. 2020;191(3):893-948. doi:10.4007/annals.2020.191.3.4
apa: Browning, T. D., & Sawin, W. (2020). A geometric version of the circle
method. Annals of Mathematics. Princeton University. https://doi.org/10.4007/annals.2020.191.3.4
chicago: Browning, Timothy D, and Will Sawin. “A Geometric Version of the Circle
Method.” Annals of Mathematics. Princeton University, 2020. https://doi.org/10.4007/annals.2020.191.3.4.
ieee: T. D. Browning and W. Sawin, “A geometric version of the circle method,” Annals
of Mathematics, vol. 191, no. 3. Princeton University, pp. 893–948, 2020.
ista: Browning TD, Sawin W. 2020. A geometric version of the circle method. Annals
of Mathematics. 191(3), 893–948.
mla: Browning, Timothy D., and Will Sawin. “A Geometric Version of the Circle Method.”
Annals of Mathematics, vol. 191, no. 3, Princeton University, 2020, pp.
893–948, doi:10.4007/annals.2020.191.3.4.
short: T.D. Browning, W. Sawin, Annals of Mathematics 191 (2020) 893–948.
date_created: 2018-12-11T11:45:02Z
date_published: 2020-05-01T00:00:00Z
date_updated: 2023-08-17T07:12:37Z
day: '01'
department:
- _id: TiBr
doi: 10.4007/annals.2020.191.3.4
external_id:
arxiv:
- '1711.10451'
isi:
- '000526986300004'
intvolume: ' 191'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1711.10451
month: '05'
oa: 1
oa_version: Preprint
page: 893-948
publication: Annals of Mathematics
publication_status: published
publisher: Princeton University
publist_id: '7744'
quality_controlled: '1'
status: public
title: A geometric version of the circle method
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 191
year: '2020'
...
---
_id: '179'
abstract:
- lang: eng
text: An asymptotic formula is established for the number of rational points of
bounded anticanonical height which lie on a certain Zariski dense subset of the
biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified
Manin conjecture for this variety, in which the removal of a thin set of rational
points is allowed.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Roger
full_name: Heath Brown, Roger
last_name: Heath Brown
citation:
ama: Browning TD, Heath Brown R. Density of rational points on a quadric bundle
in ℙ3×ℙ3. Duke Mathematical Journal. 2020;169(16):3099-3165. doi:10.1215/00127094-2020-0031
apa: Browning, T. D., & Heath Brown, R. (2020). Density of rational points on
a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. Duke University Press.
https://doi.org/10.1215/00127094-2020-0031
chicago: Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points
on a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal. Duke University
Press, 2020. https://doi.org/10.1215/00127094-2020-0031.
ieee: T. D. Browning and R. Heath Brown, “Density of rational points on a quadric
bundle in ℙ3×ℙ3,” Duke Mathematical Journal, vol. 169, no. 16. Duke University
Press, pp. 3099–3165, 2020.
ista: Browning TD, Heath Brown R. 2020. Density of rational points on a quadric
bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165.
mla: Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on
a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal, vol. 169, no. 16,
Duke University Press, 2020, pp. 3099–165, doi:10.1215/00127094-2020-0031.
short: T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165.
date_created: 2018-12-11T11:45:02Z
date_published: 2020-09-10T00:00:00Z
date_updated: 2023-10-17T12:51:10Z
day: '10'
department:
- _id: TiBr
doi: 10.1215/00127094-2020-0031
external_id:
arxiv:
- '1805.10715'
isi:
- '000582676300002'
intvolume: ' 169'
isi: 1
issue: '16'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1805.10715
month: '09'
oa: 1
oa_version: Preprint
page: 3099-3165
publication: Duke Mathematical Journal
publication_identifier:
issn:
- 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
status: public
title: Density of rational points on a quadric bundle in ℙ3×ℙ3
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 169
year: '2020'
...
---
_id: '9007'
abstract:
- lang: eng
text: Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle
method to count “sufficiently free” rational points of bounded height on arbitrary
smooth projective hypersurfaces of low degree that are defined over the rationals.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Will
full_name: Sawin, Will
last_name: Sawin
citation:
ama: Browning TD, Sawin W. Free rational points on smooth hypersurfaces. Commentarii
Mathematici Helvetici. 2020;95(4):635-659. doi:10.4171/CMH/499
apa: Browning, T. D., & Sawin, W. (2020). Free rational points on smooth hypersurfaces.
Commentarii Mathematici Helvetici. European Mathematical Society. https://doi.org/10.4171/CMH/499
chicago: Browning, Timothy D, and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.”
Commentarii Mathematici Helvetici. European Mathematical Society, 2020.
https://doi.org/10.4171/CMH/499.
ieee: T. D. Browning and W. Sawin, “Free rational points on smooth hypersurfaces,”
Commentarii Mathematici Helvetici, vol. 95, no. 4. European Mathematical
Society, pp. 635–659, 2020.
ista: Browning TD, Sawin W. 2020. Free rational points on smooth hypersurfaces.
Commentarii Mathematici Helvetici. 95(4), 635–659.
mla: Browning, Timothy D., and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.”
Commentarii Mathematici Helvetici, vol. 95, no. 4, European Mathematical
Society, 2020, pp. 635–59, doi:10.4171/CMH/499.
short: T.D. Browning, W. Sawin, Commentarii Mathematici Helvetici 95 (2020) 635–659.
date_created: 2021-01-17T23:01:11Z
date_published: 2020-12-07T00:00:00Z
date_updated: 2023-08-24T11:11:36Z
day: '07'
department:
- _id: TiBr
doi: 10.4171/CMH/499
external_id:
arxiv:
- '1906.08463'
isi:
- '000596833300001'
intvolume: ' 95'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1906.08463
month: '12'
oa: 1
oa_version: Preprint
page: 635-659
publication: Commentarii Mathematici Helvetici
publication_identifier:
eissn:
- '14208946'
issn:
- '00102571'
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Free rational points on smooth hypersurfaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 95
year: '2020'
...
---
_id: '170'
abstract:
- lang: eng
text: Upper and lower bounds, of the expected order of magnitude, are obtained for
the number of rational points of bounded height on any quartic del Pezzo surface
over ℚ that contains a conic defined over ℚ .
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Efthymios
full_name: Sofos, Efthymios
last_name: Sofos
citation:
ama: Browning TD, Sofos E. Counting rational points on quartic del Pezzo surfaces
with a rational conic. Mathematische Annalen. 2019;373(3-4):977-1016. doi:10.1007/s00208-018-1716-6
apa: Browning, T. D., & Sofos, E. (2019). Counting rational points on quartic
del Pezzo surfaces with a rational conic. Mathematische Annalen. Springer
Nature. https://doi.org/10.1007/s00208-018-1716-6
chicago: Browning, Timothy D, and Efthymios Sofos. “Counting Rational Points on
Quartic Del Pezzo Surfaces with a Rational Conic.” Mathematische Annalen.
Springer Nature, 2019. https://doi.org/10.1007/s00208-018-1716-6.
ieee: T. D. Browning and E. Sofos, “Counting rational points on quartic del Pezzo
surfaces with a rational conic,” Mathematische Annalen, vol. 373, no. 3–4.
Springer Nature, pp. 977–1016, 2019.
ista: Browning TD, Sofos E. 2019. Counting rational points on quartic del Pezzo
surfaces with a rational conic. Mathematische Annalen. 373(3–4), 977–1016.
mla: Browning, Timothy D., and Efthymios Sofos. “Counting Rational Points on Quartic
Del Pezzo Surfaces with a Rational Conic.” Mathematische Annalen, vol.
373, no. 3–4, Springer Nature, 2019, pp. 977–1016, doi:10.1007/s00208-018-1716-6.
short: T.D. Browning, E. Sofos, Mathematische Annalen 373 (2019) 977–1016.
date_created: 2018-12-11T11:44:59Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2021-01-12T06:52:37Z
day: '01'
ddc:
- '510'
doi: 10.1007/s00208-018-1716-6
extern: '1'
external_id:
arxiv:
- '1609.09057'
file:
- access_level: open_access
checksum: 4061dc2fe99bee25d9adf2d2018cf608
content_type: application/pdf
creator: dernst
date_created: 2019-05-23T07:53:27Z
date_updated: 2020-07-14T12:45:12Z
file_id: '6479'
file_name: 2019_MathAnnalen_Browning.pdf
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- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 977-1016
publication: Mathematische Annalen
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Counting rational points on quartic del Pezzo surfaces with a rational conic
tmp:
image: /images/cc_by.png
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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...
---
_id: '175'
abstract:
- lang: eng
text: An upper bound sieve for rational points on suitable varieties isdeveloped,
together with applications tocounting rational points in thin sets,to local solubility
in families, and to the notion of “friable” rational pointswith respect to divisors.
In the special case of quadrics, sharper estimates areobtained by developing a
version of the Selberg sieve for rational points.
article_processing_charge: No
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Daniel
full_name: Loughran, Daniel
last_name: Loughran
citation:
ama: Browning TD, Loughran D. Sieving rational points on varieties. Transactions
of the American Mathematical Society. 2019;371(8):5757-5785. doi:10.1090/tran/7514
apa: Browning, T. D., & Loughran, D. (2019). Sieving rational points on varieties.
Transactions of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/tran/7514
chicago: Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.”
Transactions of the American Mathematical Society. American Mathematical
Society, 2019. https://doi.org/10.1090/tran/7514.
ieee: T. D. Browning and D. Loughran, “Sieving rational points on varieties,” Transactions
of the American Mathematical Society, vol. 371, no. 8. American Mathematical
Society, pp. 5757–5785, 2019.
ista: Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions
of the American Mathematical Society. 371(8), 5757–5785.
mla: Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.”
Transactions of the American Mathematical Society, vol. 371, no. 8, American
Mathematical Society, 2019, pp. 5757–85, doi:10.1090/tran/7514.
short: T.D. Browning, D. Loughran, Transactions of the American Mathematical Society
371 (2019) 5757–5785.
date_created: 2018-12-11T11:45:01Z
date_published: 2019-04-15T00:00:00Z
date_updated: 2023-08-24T14:34:56Z
day: '15'
department:
- _id: TiBr
doi: 10.1090/tran/7514
external_id:
arxiv:
- '1705.01999'
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- '000464034200019'
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isi: 1
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- iso: eng
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- open_access: '1'
url: https://arxiv.org/abs/1705.01999
month: '04'
oa: 1
oa_version: Preprint
page: 5757-5785
publication: Transactions of the American Mathematical Society
publication_identifier:
eissn:
- '10886850'
issn:
- '00029947'
publication_status: published
publisher: American Mathematical Society
publist_id: '7746'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sieving rational points on varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 371
year: '2019'
...
---
_id: '6310'
abstract:
- lang: eng
text: An asymptotic formula is established for the number of rational points of
bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary
smooth biquadratic hypersurface in sufficiently many variables. The proof uses
the Hardy–Littlewood circle method.
article_processing_charge: No
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: L.Q.
full_name: Hu, L.Q.
last_name: Hu
citation:
ama: Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces.
Advances in Mathematics. 2019;349:920-940. doi:10.1016/j.aim.2019.04.031
apa: Browning, T. D., & Hu, L. Q. (2019). Counting rational points on biquadratic
hypersurfaces. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2019.04.031
chicago: Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic
Hypersurfaces.” Advances in Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.aim.2019.04.031.
ieee: T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,”
Advances in Mathematics, vol. 349. Elsevier, pp. 920–940, 2019.
ista: Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces.
Advances in Mathematics. 349, 920–940.
mla: Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic
Hypersurfaces.” Advances in Mathematics, vol. 349, Elsevier, 2019, pp.
920–40, doi:10.1016/j.aim.2019.04.031.
short: T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940.
date_created: 2019-04-16T09:13:25Z
date_published: 2019-06-20T00:00:00Z
date_updated: 2023-08-25T10:11:55Z
day: '20'
ddc:
- '512'
department:
- _id: TiBr
doi: 10.1016/j.aim.2019.04.031
external_id:
arxiv:
- '1810.08426'
isi:
- '000468857300025'
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creator: tbrownin
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issn:
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publication_status: published
publisher: Elsevier
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title: Counting rational points on biquadratic hypersurfaces
type: journal_article
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volume: 349
year: '2019'
...
---
_id: '174'
abstract:
- lang: eng
text: We survey recent efforts to quantify failures of the Hasse principle in families
of rationally connected varieties.
alternative_title:
- Proceedings of Symposia in Pure Mathematics
article_processing_charge: No
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
citation:
ama: 'Browning TD. How often does the Hasse principle hold? In: Vol 97. American
Mathematical Society; 2018:89-102. doi:10.1090/pspum/097.2/01700'
apa: 'Browning, T. D. (2018). How often does the Hasse principle hold? (Vol. 97,
pp. 89–102). Presented at the Algebraic Geometry, Salt Lake City, Utah, USA: American
Mathematical Society. https://doi.org/10.1090/pspum/097.2/01700'
chicago: Browning, Timothy D. “How Often Does the Hasse Principle Hold?,” 97:89–102.
American Mathematical Society, 2018. https://doi.org/10.1090/pspum/097.2/01700.
ieee: T. D. Browning, “How often does the Hasse principle hold?,” presented at the
Algebraic Geometry, Salt Lake City, Utah, USA, 2018, vol. 97, no. 2, pp. 89–102.
ista: Browning TD. 2018. How often does the Hasse principle hold? Algebraic Geometry,
Proceedings of Symposia in Pure Mathematics, vol. 97, 89–102.
mla: Browning, Timothy D. How Often Does the Hasse Principle Hold? Vol. 97,
no. 2, American Mathematical Society, 2018, pp. 89–102, doi:10.1090/pspum/097.2/01700.
short: T.D. Browning, in:, American Mathematical Society, 2018, pp. 89–102.
conference:
end_date: 2015-07-10
location: Salt Lake City, Utah, USA
name: Algebraic Geometry
start_date: 2015-07-06
date_created: 2018-12-11T11:45:01Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2021-01-12T06:52:54Z
day: '01'
doi: 10.1090/pspum/097.2/01700
extern: '1'
intvolume: ' 97'
issue: '2'
language:
- iso: eng
month: '01'
oa_version: None
page: 89 - 102
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: How often does the Hasse principle hold?
type: conference
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 97
year: '2018'
...
---
_id: '176'
abstract:
- lang: eng
text: For a general class of non-negative functions defined on integral ideals of
number fields, upper bounds are established for their average over the values
of certain principal ideals that are associated to irreducible binary forms with
integer coefficients.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Efthymios
full_name: Sofos, Efthymios
last_name: Sofos
citation:
ama: Browning TD, Sofos E. Averages of arithmetic functions over principal ideals.
International Journal of Nuber Theory. 2018;15(3):547-567. doi:10.1142/S1793042119500283
apa: Browning, T. D., & Sofos, E. (2018). Averages of arithmetic functions over
principal ideals. International Journal of Nuber Theory. World Scientific
Publishing. https://doi.org/10.1142/S1793042119500283
chicago: Browning, Timothy D, and Efthymios Sofos. “Averages of Arithmetic Functions
over Principal Ideals.” International Journal of Nuber Theory. World Scientific
Publishing, 2018. https://doi.org/10.1142/S1793042119500283.
ieee: T. D. Browning and E. Sofos, “Averages of arithmetic functions over principal
ideals,” International Journal of Nuber Theory, vol. 15, no. 3. World Scientific
Publishing, pp. 547–567, 2018.
ista: Browning TD, Sofos E. 2018. Averages of arithmetic functions over principal
ideals. International Journal of Nuber Theory. 15(3), 547–567.
mla: Browning, Timothy D., and Efthymios Sofos. “Averages of Arithmetic Functions
over Principal Ideals.” International Journal of Nuber Theory, vol. 15,
no. 3, World Scientific Publishing, 2018, pp. 547–67, doi:10.1142/S1793042119500283.
short: T.D. Browning, E. Sofos, International Journal of Nuber Theory 15 (2018)
547–567.
date_created: 2018-12-11T11:45:01Z
date_published: 2018-11-16T00:00:00Z
date_updated: 2021-01-12T06:53:01Z
day: '16'
doi: 10.1142/S1793042119500283
extern: '1'
external_id:
arxiv:
- '1706.04331'
intvolume: ' 15'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.04331
month: '11'
oa: 1
oa_version: Preprint
page: 547-567
publication: International Journal of Nuber Theory
publication_status: published
publisher: World Scientific Publishing
status: public
title: Averages of arithmetic functions over principal ideals
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 15
year: '2018'
...
---
_id: '178'
abstract:
- lang: eng
text: We give an upper bound for the number of rational points of height at most
B, lying on a surface defined by a quadratic form Q. The bound shows an explicit
dependence on Q. It is optimal with respect to B, and is also optimal for typical
forms Q.
article_processing_charge: No
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Roger
full_name: Heath-Brown, Roger
last_name: Heath-Brown
citation:
ama: Browning TD, Heath-Brown R. Counting rational points on quadric surfaces. Discrete
Analysis. 2018;15:1-29. doi:10.19086/da.4375
apa: Browning, T. D., & Heath-Brown, R. (2018). Counting rational points on
quadric surfaces. Discrete Analysis. Alliance of Diamond Open Access Journals.
https://doi.org/10.19086/da.4375
chicago: Browning, Timothy D, and Roger Heath-Brown. “Counting Rational Points on
Quadric Surfaces.” Discrete Analysis. Alliance of Diamond Open Access Journals,
2018. https://doi.org/10.19086/da.4375.
ieee: T. D. Browning and R. Heath-Brown, “Counting rational points on quadric surfaces,”
Discrete Analysis, vol. 15. Alliance of Diamond Open Access Journals, pp.
1–29, 2018.
ista: Browning TD, Heath-Brown R. 2018. Counting rational points on quadric surfaces.
Discrete Analysis. 15, 1–29.
mla: Browning, Timothy D., and Roger Heath-Brown. “Counting Rational Points on Quadric
Surfaces.” Discrete Analysis, vol. 15, Alliance of Diamond Open Access
Journals, 2018, pp. 1–29, doi:10.19086/da.4375.
short: T.D. Browning, R. Heath-Brown, Discrete Analysis 15 (2018) 1–29.
date_created: 2018-12-11T11:45:02Z
date_published: 2018-09-07T00:00:00Z
date_updated: 2022-08-26T09:13:02Z
day: '07'
ddc:
- '512'
doi: 10.19086/da.4375
extern: '1'
external_id:
arxiv:
- '1801.00979'
intvolume: ' 15'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1801.00979
month: '09'
oa: 1
oa_version: Preprint
page: 1 - 29
publication: Discrete Analysis
publication_identifier:
eissn:
- 2397-3129
publication_status: published
publisher: Alliance of Diamond Open Access Journals
quality_controlled: '1'
status: public
title: Counting rational points on quadric surfaces
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2018'
...
---
_id: '256'
abstract:
- lang: eng
text: We show that a non-singular integral form of degree d is soluble over the
integers if and only if it is soluble over ℝ and over ℚp for all primes p, provided
that the form has at least (d - 1/2 √d)2d variables. This improves on a longstanding
result of Birch.
acknowledgement: While working on this paper the authors were supported by the Leverhulme
Trust and ERC grant 306457.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Sean
full_name: Prendiville, Sean
last_name: Prendiville
citation:
ama: Browning TD, Prendiville S. Improvements in Birch’s theorem on forms in many
variables. Journal fur die Reine und Angewandte Mathematik. 2017;2017(731):122.
doi:10.1515/crelle-2014-0122
apa: Browning, T. D., & Prendiville, S. (2017). Improvements in Birch’s theorem
on forms in many variables. Journal Fur Die Reine Und Angewandte Mathematik.
Walter de Gruyter. https://doi.org/10.1515/crelle-2014-0122
chicago: Browning, Timothy D, and Sean Prendiville. “Improvements in Birch’s Theorem
on Forms in Many Variables.” Journal Fur Die Reine Und Angewandte Mathematik.
Walter de Gruyter, 2017. https://doi.org/10.1515/crelle-2014-0122.
ieee: T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms
in many variables,” Journal fur die Reine und Angewandte Mathematik, vol.
2017, no. 731. Walter de Gruyter, p. 122, 2017.
ista: Browning TD, Prendiville S. 2017. Improvements in Birch’s theorem on forms
in many variables. Journal fur die Reine und Angewandte Mathematik. 2017(731),
122.
mla: Browning, Timothy D., and Sean Prendiville. “Improvements in Birch’s Theorem
on Forms in Many Variables.” Journal Fur Die Reine Und Angewandte Mathematik,
vol. 2017, no. 731, Walter de Gruyter, 2017, p. 122, doi:10.1515/crelle-2014-0122.
short: T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik
2017 (2017) 122.
date_created: 2018-12-11T11:45:28Z
date_published: 2017-10-01T00:00:00Z
date_updated: 2024-03-05T12:09:21Z
day: '01'
doi: 10.1515/crelle-2014-0122
extern: '1'
external_id:
arxiv:
- '1402.4489'
intvolume: ' 2017'
issue: '731'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1402.4489
month: '10'
oa: 1
oa_version: Preprint
page: '122'
publication: Journal fur die Reine und Angewandte Mathematik
publication_identifier:
issn:
- 0075-4102
publication_status: published
publisher: Walter de Gruyter
publist_id: '7646'
quality_controlled: '1'
related_material:
record:
- id: '271'
relation: earlier_version
status: public
status: public
title: Improvements in Birch's theorem on forms in many variables
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2017
year: '2017'
...
---
_id: '265'
abstract:
- lang: eng
text: We establish the dimension and irreducibility of the moduli space of rational
curves (of fixed degree) on arbitrary smooth hypersurfaces of sufficiently low
degree. A spreading out argument reduces the problem to hypersurfaces defined
over finite fields of large cardinality, which can then be tackled using a function
field version of the Hardy-Littlewood circle method, in which particular care
is taken to ensure uniformity in the size of the underlying finite field.
acknowledgement: While working on this paper the first author was supported by ERC
grant 306457.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Pankaj
full_name: Vishe, Pankaj
last_name: Vishe
citation:
ama: Browning TD, Vishe P. Rational curves on smooth hypersurfaces of low degree.
Geometric Methods in Algebra and Number Theory. 2017;11(7):1657-1675. doi:10.2140/ant.2017.11.1657
apa: Browning, T. D., & Vishe, P. (2017). Rational curves on smooth hypersurfaces
of low degree. Geometric Methods in Algebra and Number Theory. Mathematical
Sciences Publishers. https://doi.org/10.2140/ant.2017.11.1657
chicago: Browning, Timothy D, and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces
of Low Degree.” Geometric Methods in Algebra and Number Theory. Mathematical
Sciences Publishers, 2017. https://doi.org/10.2140/ant.2017.11.1657.
ieee: T. D. Browning and P. Vishe, “Rational curves on smooth hypersurfaces of low
degree,” Geometric Methods in Algebra and Number Theory, vol. 11, no. 7. Mathematical
Sciences Publishers, pp. 1657–1675, 2017.
ista: Browning TD, Vishe P. 2017. Rational curves on smooth hypersurfaces of low
degree. Geometric Methods in Algebra and Number Theory. 11(7), 1657–1675.
mla: Browning, Timothy D., and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces
of Low Degree.” Geometric Methods in Algebra and Number Theory, vol. 11,
no. 7, Mathematical Sciences Publishers, 2017, pp. 1657–75, doi:10.2140/ant.2017.11.1657.
short: T.D. Browning, P. Vishe, Geometric Methods in Algebra and Number Theory 11
(2017) 1657–1675.
date_created: 2018-12-11T11:45:30Z
date_published: 2017-09-07T00:00:00Z
date_updated: 2024-03-05T11:43:38Z
day: '07'
doi: 10.2140/ant.2017.11.1657
extern: '1'
external_id:
arxiv:
- '1611.00553'
intvolume: ' 11'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1611.00553
month: '09'
oa: 1
oa_version: Preprint
page: 1657 - 1675
publication: Geometric Methods in Algebra and Number Theory
publication_identifier:
eissn:
- 1944-7833
publication_status: published
publisher: ' Mathematical Sciences Publishers'
publist_id: '7637'
quality_controlled: '1'
status: public
title: Rational curves on smooth hypersurfaces of low degree
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2017'
...