[{"author":[{"full_name":"Cao, Yang","first_name":"Yang","last_name":"Cao"},{"id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","last_name":"Huang","first_name":"Zhizhong","full_name":"Huang, Zhizhong"}],"oa":1,"_id":"10765","date_published":"2022-03-26T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2022.108236","publisher":"Elsevier","year":"2022","type":"journal_article","month":"03","quality_controlled":"1","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"isi":1,"volume":398,"article_type":"original","article_number":"108236","date_created":"2022-02-20T23:01:30Z","acknowledgement":"We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg for their interest in our\r\nwork. We would like to address our gratitude to Ulrich Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt to Tim Browning for an enlightening discussion and to the anonymous referees for critical comments, which lead to overall improvements of various preliminary versions of this paper. Part of this work was carried out and reported during a visit to the University of Science and Technology of China. We thank Yongqi Liang for offering warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium. The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft.","department":[{"_id":"TiBr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","intvolume":"       398","oa_version":"Preprint","publication_status":"published","day":"26","abstract":[{"lang":"eng","text":"We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate integral quadratic form in  n>3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics."}],"date_updated":"2023-08-02T14:24:18Z","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/2003.07287","open_access":"1"}],"publication":"Advances in Mathematics","external_id":{"arxiv":["2003.07287"],"isi":["000792517300014"]},"title":"Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics","arxiv":1,"citation":{"ama":"Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. 2022;398(3). doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>","mla":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>, vol. 398, no. 3, 108236, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>.","ista":"Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.","short":"Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).","apa":"Cao, Y., &#38; Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>","ieee":"Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics,” <i>Advances in Mathematics</i>, vol. 398, no. 3. Elsevier, 2022.","chicago":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>."},"issue":"3","scopus_import":"1"},{"_id":"10033","oa":1,"author":[{"last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6889-1418","first_name":"Quoc P","full_name":"Ho, Quoc P"}],"date_published":"2021-09-21T00:00:00Z","year":"2021","publisher":"Elsevier","doi":"10.1016/j.aim.2021.107992","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"quality_controlled":"1","month":"09","volume":392,"article_type":"original","isi":1,"acknowledgement":"The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.","department":[{"_id":"TaHa"}],"article_number":"107992","date_created":"2021-09-21T15:58:59Z","intvolume":"       392","keyword":["Chiral algebras","Chiral homology","Factorization algebras","Koszul duality","Ran space"],"file_date_updated":"2021-09-21T15:58:52Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","ddc":["514"],"abstract":[{"text":"The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5].","lang":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"21","oa_version":"Published Version","publication_status":"published","date_updated":"2023-08-14T06:54:35Z","status":"public","file":[{"creator":"qho","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"1-s2.0-S000187082100431X-main.pdf","file_size":840635,"checksum":"f3c0086d41af11db31c00014efb38072","date_created":"2021-09-21T15:58:52Z","file_id":"10034","date_updated":"2021-09-21T15:58:52Z"}],"title":"The Atiyah-Bott formula and connectivity in chiral Koszul duality","external_id":{"isi":["000707040300031"],"arxiv":["1610.00212"]},"publication":"Advances in Mathematics","arxiv":1,"citation":{"ama":"Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. 2021;392. doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>","apa":"Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>","mla":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>, vol. 392, 107992, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>.","ista":"Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992.","short":"Q.P. Ho, Advances in Mathematics 392 (2021).","ieee":"Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” <i>Advances in Mathematics</i>, vol. 392. Elsevier, 2021.","chicago":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>."},"project":[{"_id":"26B96266-B435-11E9-9278-68D0E5697425","name":"Algebro-Geometric Applications of Factorization Homology","call_identifier":"FWF","grant_number":"M02751"}],"has_accepted_license":"1","scopus_import":"1"}]