--- _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 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. Archiv der Mathematik. 2021;116(5):515-527. doi:10.1007/s00013-020-01564-y apa: Srivastava, T. K. (2021). Lifting automorphisms on Abelian varieties as derived autoequivalences. Archiv Der Mathematik. Springer Nature. https://doi.org/10.1007/s00013-020-01564-y chicago: Srivastava, Tanya K. “Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences.” Archiv Der Mathematik. Springer Nature, 2021. https://doi.org/10.1007/s00013-020-01564-y. ieee: T. K. Srivastava, “Lifting automorphisms on Abelian varieties as derived autoequivalences,” Archiv der Mathematik, 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.” Archiv Der Mathematik, vol. 116, no. 5, Springer Nature, 2021, pp. 515–27, doi:10.1007/s00013-020-01564-y. 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 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. Bulletin des Sciences Mathematiques. 2021;167(03). doi:10.1016/j.bulsci.2021.102957 apa: Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin Des Sciences Mathematiques. Elsevier. https://doi.org/10.1016/j.bulsci.2021.102957 chicago: Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” Bulletin Des Sciences Mathematiques. Elsevier, 2021. https://doi.org/10.1016/j.bulsci.2021.102957. ieee: T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular Enriques surface,” Bulletin des Sciences Mathematiques, 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.” Bulletin Des Sciences Mathematiques, vol. 167, no. 03, 102957, Elsevier, 2021, doi:10.1016/j.bulsci.2021.102957. 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 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. Documenta Mathematica. 2019;24:1135-1177. doi:10.25537/dm.2019v24.1135-1177 apa: Srivastava, T. K. (2019). On derived equivalences of k3 surfaces in positive characteristic. Documenta Mathematica. EMS Press. https://doi.org/10.25537/dm.2019v24.1135-1177 chicago: Srivastava, Tanya K. “On Derived Equivalences of K3 Surfaces in Positive Characteristic.” Documenta Mathematica. EMS Press, 2019. https://doi.org/10.25537/dm.2019v24.1135-1177. ieee: T. K. Srivastava, “On derived equivalences of k3 surfaces in positive characteristic,” Documenta Mathematica, 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.” Documenta Mathematica, vol. 24, EMS Press, 2019, pp. 1135–77, doi:10.25537/dm.2019v24.1135-1177. 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 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: 24 year: '2019' ...