[{"publication_identifier":{"issn":["0003889X"],"eissn":["14208938"]},"publication_status":"published","intvolume":"       116","abstract":[{"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.","lang":"eng"}],"volume":116,"article_type":"original","date_created":"2021-02-07T23:01:13Z","author":[{"last_name":"Srivastava","full_name":"Srivastava, Tanya K","id":"4D046628-F248-11E8-B48F-1D18A9856A87","first_name":"Tanya K"}],"scopus_import":"1","day":"01","title":"Lifting automorphisms on Abelian varieties as derived autoequivalences","oa_version":"Preprint","issue":"5","citation":{"short":"T.K. Srivastava, Archiv Der Mathematik 116 (2021) 515–527.","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.","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>","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>.","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>","ista":"Srivastava TK. 2021. Lifting automorphisms on Abelian varieties as derived autoequivalences. Archiv der Mathematik. 116(5), 515–527.","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>."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"TaHa"}],"arxiv":1,"month":"05","main_file_link":[{"url":"https://arxiv.org/abs/2001.07762","open_access":"1"}],"quality_controlled":"1","page":"515-527","date_updated":"2023-08-07T13:42:38Z","_id":"9099","type":"journal_article","doi":"10.1007/s00013-020-01564-y","article_processing_charge":"No","publisher":"Springer Nature","ec_funded":1,"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.","date_published":"2021-05-01T00:00:00Z","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"status":"public","publication":"Archiv der Mathematik","year":"2021","isi":1,"external_id":{"arxiv":["2001.07762"],"isi":["000612580200001"]}},{"citation":{"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.","short":"T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021).","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>","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>.","ista":"Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957.","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>."},"issue":"03","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"language":[{"iso":"eng"}],"department":[{"_id":"TaHa"}],"article_number":"102957","arxiv":1,"month":"03","publication_status":"published","publication_identifier":{"issn":["0007-4497"]},"abstract":[{"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.","lang":"eng"}],"intvolume":"       167","volume":167,"date_created":"2021-02-21T23:01:20Z","article_type":"original","scopus_import":"1","day":"01","author":[{"full_name":"Srivastava, Tanya K","id":"4D046628-F248-11E8-B48F-1D18A9856A87","last_name":"Srivastava","first_name":"Tanya K"}],"oa_version":"Preprint","title":"Pathologies of the Hilbert scheme of points of a supersingular Enriques surface","ec_funded":1,"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.","date_published":"2021-03-01T00:00:00Z","status":"public","publication":"Bulletin des Sciences Mathematiques","project":[{"call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"isi":1,"year":"2021","external_id":{"isi":["000623881600009"],"arxiv":["2010.08976"]},"main_file_link":[{"url":"https://arxiv.org/abs/2010.08976","open_access":"1"}],"quality_controlled":"1","_id":"9173","date_updated":"2023-08-07T13:47:48Z","type":"journal_article","article_processing_charge":"No","doi":"10.1016/j.bulsci.2021.102957","publisher":"Elsevier"},{"department":[{"_id":"TaHa"}],"file":[{"file_size":469730,"date_created":"2020-02-03T06:26:12Z","date_updated":"2020-07-14T12:47:58Z","creator":"dernst","file_id":"7438","file_name":"2019_DocumMath_Srivastava.pdf","access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"9a1a64bd49ab03fa4f738fb250fc4f90"}],"arxiv":1,"month":"05","citation":{"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>","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>.","ista":"Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic. Documenta Mathematica. 24, 1135–1177.","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.","short":"T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177.","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>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"volume":24,"article_type":"original","date_created":"2020-02-02T23:01:06Z","author":[{"first_name":"Tanya K","full_name":"Srivastava, Tanya K","id":"4D046628-F248-11E8-B48F-1D18A9856A87","last_name":"Srivastava"}],"scopus_import":"1","day":"20","title":"On derived equivalences of k3 surfaces in positive characteristic","oa_version":"Published Version","publication_identifier":{"issn":["1431-0635"],"eissn":["1431-0643"]},"publication_status":"published","file_date_updated":"2020-07-14T12:47:58Z","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"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. ","lang":"eng"}],"intvolume":"        24","isi":1,"year":"2019","external_id":{"isi":["000517806400019"],"arxiv":["1809.08970"]},"date_published":"2019-05-20T00:00:00Z","publication":"Documenta Mathematica","status":"public","date_updated":"2023-10-17T07:42:21Z","_id":"7436","type":"journal_article","doi":"10.25537/dm.2019v24.1135-1177","article_processing_charge":"No","publisher":"EMS Press","quality_controlled":"1","page":"1135-1177","ddc":["510"]}]