---
_id: '9099'
abstract:
- lang: eng
  text: We show that on an Abelian variety over an algebraically closed field of positive
    characteristic, the obstruction to lifting an automorphism to a field of characteristic
    zero as a morphism vanishes if and only if it vanishes for lifting it as a derived
    autoequivalence. We also compare the deformation space of these two types of deformations.
acknowledgement: I would like to thank Piotr Achinger, Daniel Huybrechts, Katrina
  Honigs, Marcin Lara, and Maciek Zdanowicz for the mathematical discussions, Tamas
  Hausel for hosting me in his research group at IST Austria, and the referees for
  their valuable suggestions. This research has received funding from the European
  Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie
  Grant Agreement No. 754411.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tanya K
  full_name: Srivastava, Tanya K
  id: 4D046628-F248-11E8-B48F-1D18A9856A87
  last_name: Srivastava
citation:
  ama: Srivastava TK. Lifting automorphisms on Abelian varieties as derived autoequivalences.
    <i>Archiv der Mathematik</i>. 2021;116(5):515-527. doi:<a href="https://doi.org/10.1007/s00013-020-01564-y">10.1007/s00013-020-01564-y</a>
  apa: Srivastava, T. K. (2021). Lifting automorphisms on Abelian varieties as derived
    autoequivalences. <i>Archiv Der Mathematik</i>. Springer Nature. <a href="https://doi.org/10.1007/s00013-020-01564-y">https://doi.org/10.1007/s00013-020-01564-y</a>
  chicago: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived
    Autoequivalences.” <i>Archiv Der Mathematik</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s00013-020-01564-y">https://doi.org/10.1007/s00013-020-01564-y</a>.
  ieee: T. K. Srivastava, “Lifting automorphisms on Abelian varieties as derived autoequivalences,”
    <i>Archiv der Mathematik</i>, vol. 116, no. 5. Springer Nature, pp. 515–527, 2021.
  ista: Srivastava TK. 2021. Lifting automorphisms on Abelian varieties as derived
    autoequivalences. Archiv der Mathematik. 116(5), 515–527.
  mla: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived
    Autoequivalences.” <i>Archiv Der Mathematik</i>, vol. 116, no. 5, Springer Nature,
    2021, pp. 515–27, doi:<a href="https://doi.org/10.1007/s00013-020-01564-y">10.1007/s00013-020-01564-y</a>.
  short: T.K. Srivastava, Archiv Der Mathematik 116 (2021) 515–527.
date_created: 2021-02-07T23:01:13Z
date_published: 2021-05-01T00:00:00Z
date_updated: 2023-08-07T13:42:38Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00013-020-01564-y
ec_funded: 1
external_id:
  arxiv:
  - '2001.07762'
  isi:
  - '000612580200001'
intvolume: '       116'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2001.07762
month: '05'
oa: 1
oa_version: Preprint
page: 515-527
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Archiv der Mathematik
publication_identifier:
  eissn:
  - '14208938'
  issn:
  - 0003889X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lifting automorphisms on Abelian varieties as derived autoequivalences
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 116
year: '2021'
...
---
_id: '9173'
abstract:
- lang: eng
  text: We show that Hilbert schemes of points on supersingular Enriques surface in
    characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties
    but are not irreducible symplectic as the hodge number h2,0 > 1, even though a
    supersingular Enriques surface is an irreducible symplectic variety. These are
    the classes of varieties which appear only in characteristic 2 and they show that
    the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic
    2. It also gives examples of varieties with trivial canonical class which are
    neither irreducible symplectic nor Calabi-Yau, thereby showing that there are
    strictly more classes of simply connected varieties with trivial canonical class
    in characteristic 2 than over C as given by Beauville-Bogolomov decomposition
    theorem.
acknowledgement: I would like to thank M. Zdanwociz for various mathematical discussions
  which lead to this article, Tamas Hausel for hosting me in his research group at
  IST Austria and the anonymous referee for their helpful suggestions and comments.
  This research has received funding from the European Union's Horizon 2020 Marie
  Sklodowska-Curie Actions Grant No. 754411 and Institue of Science and Technology
  Austria IST-PLUS Grant No. 754411.
article_number: '102957'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tanya K
  full_name: Srivastava, Tanya K
  id: 4D046628-F248-11E8-B48F-1D18A9856A87
  last_name: Srivastava
citation:
  ama: Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular
    Enriques surface. <i>Bulletin des Sciences Mathematiques</i>. 2021;167(03). doi:<a
    href="https://doi.org/10.1016/j.bulsci.2021.102957">10.1016/j.bulsci.2021.102957</a>
  apa: Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a
    supersingular Enriques surface. <i>Bulletin Des Sciences Mathematiques</i>. Elsevier.
    <a href="https://doi.org/10.1016/j.bulsci.2021.102957">https://doi.org/10.1016/j.bulsci.2021.102957</a>
  chicago: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a
    Supersingular Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>. Elsevier,
    2021. <a href="https://doi.org/10.1016/j.bulsci.2021.102957">https://doi.org/10.1016/j.bulsci.2021.102957</a>.
  ieee: T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular
    Enriques surface,” <i>Bulletin des Sciences Mathematiques</i>, vol. 167, no. 03.
    Elsevier, 2021.
  ista: Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular
    Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957.
  mla: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular
    Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>, vol. 167, no. 03,
    102957, Elsevier, 2021, doi:<a href="https://doi.org/10.1016/j.bulsci.2021.102957">10.1016/j.bulsci.2021.102957</a>.
  short: T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021).
date_created: 2021-02-21T23:01:20Z
date_published: 2021-03-01T00:00:00Z
date_updated: 2023-08-07T13:47:48Z
day: '01'
department:
- _id: TaHa
doi: 10.1016/j.bulsci.2021.102957
ec_funded: 1
external_id:
  arxiv:
  - '2010.08976'
  isi:
  - '000623881600009'
intvolume: '       167'
isi: 1
issue: '03'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2010.08976
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Bulletin des Sciences Mathematiques
publication_identifier:
  issn:
  - 0007-4497
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pathologies of the Hilbert scheme of points of a supersingular Enriques surface
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 167
year: '2021'
...
---
_id: '7436'
abstract:
- lang: eng
  text: 'For an ordinary K3 surface over an algebraically closed field of positive
    characteristic we show that every automorphism lifts to characteristic zero. Moreover,
    we show that the Fourier-Mukai partners of an ordinary K3 surface are in one-to-one
    correspondence with the Fourier-Mukai partners of the geometric generic fiber
    of its canonical lift. We also prove that the explicit counting formula for Fourier-Mukai
    partners of the K3 surfaces with Picard rank two and with discriminant equal to
    minus of a prime number, in terms of the class number of the prime, holds over
    a field of positive characteristic as well. We show that the image of the derived
    autoequivalence group of a K3 surface of finite height in the group of isometries
    of its crystalline cohomology has index at least two. Moreover, we provide a conditional
    upper bound on the kernel of this natural cohomological descent map. Further,
    we give an extended remark in the appendix on the possibility of an F-crystal
    structure on the crystalline cohomology of a K3 surface over an algebraically
    closed field of positive characteristic and show that the naive F-crystal structure
    fails in being compatible with inner product. '
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tanya K
  full_name: Srivastava, Tanya K
  id: 4D046628-F248-11E8-B48F-1D18A9856A87
  last_name: Srivastava
citation:
  ama: Srivastava TK. On derived equivalences of k3 surfaces in positive characteristic.
    <i>Documenta Mathematica</i>. 2019;24:1135-1177. doi:<a href="https://doi.org/10.25537/dm.2019v24.1135-1177">10.25537/dm.2019v24.1135-1177</a>
  apa: Srivastava, T. K. (2019). On derived equivalences of k3 surfaces in positive
    characteristic. <i>Documenta Mathematica</i>. EMS Press. <a href="https://doi.org/10.25537/dm.2019v24.1135-1177">https://doi.org/10.25537/dm.2019v24.1135-1177</a>
  chicago: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive
    Characteristic.” <i>Documenta Mathematica</i>. EMS Press, 2019. <a href="https://doi.org/10.25537/dm.2019v24.1135-1177">https://doi.org/10.25537/dm.2019v24.1135-1177</a>.
  ieee: T. K. Srivastava, “On derived equivalences of k3 surfaces in positive characteristic,”
    <i>Documenta Mathematica</i>, vol. 24. EMS Press, pp. 1135–1177, 2019.
  ista: Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic.
    Documenta Mathematica. 24, 1135–1177.
  mla: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.”
    <i>Documenta Mathematica</i>, vol. 24, EMS Press, 2019, pp. 1135–77, doi:<a href="https://doi.org/10.25537/dm.2019v24.1135-1177">10.25537/dm.2019v24.1135-1177</a>.
  short: T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177.
date_created: 2020-02-02T23:01:06Z
date_published: 2019-05-20T00:00:00Z
date_updated: 2023-10-17T07:42:21Z
day: '20'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.25537/dm.2019v24.1135-1177
external_id:
  arxiv:
  - '1809.08970'
  isi:
  - '000517806400019'
file:
- access_level: open_access
  checksum: 9a1a64bd49ab03fa4f738fb250fc4f90
  content_type: application/pdf
  creator: dernst
  date_created: 2020-02-03T06:26:12Z
  date_updated: 2020-07-14T12:47:58Z
  file_id: '7438'
  file_name: 2019_DocumMath_Srivastava.pdf
  file_size: 469730
  relation: main_file
file_date_updated: 2020-07-14T12:47:58Z
has_accepted_license: '1'
intvolume: '        24'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1135-1177
publication: Documenta Mathematica
publication_identifier:
  eissn:
  - 1431-0643
  issn:
  - 1431-0635
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On derived equivalences of k3 surfaces in positive characteristic
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  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
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...