{"publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"ddc":["510"],"year":"2019","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"}],"publisher":"EMS Press","article_type":"original","status":"public","department":[{"_id":"TaHa"}],"oa_version":"Published Version","type":"journal_article","citation":{"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>.","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.","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>","ista":"Srivastava TK. 2019. On derived equivalences of k3 surfaces in positive characteristic. Documenta Mathematica. 24, 1135–1177.","short":"T.K. Srivastava, Documenta Mathematica 24 (2019) 1135–1177.","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>."},"has_accepted_license":"1","date_created":"2020-02-02T23:01:06Z","scopus_import":"1","isi":1,"article_processing_charge":"No","title":"On derived equivalences of k3 surfaces in positive characteristic","month":"05","date_updated":"2023-10-17T07:42:21Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","language":[{"iso":"eng"}],"license":"https://creativecommons.org/licenses/by/4.0/","intvolume":"        24","file":[{"date_created":"2020-02-03T06:26:12Z","file_id":"7438","checksum":"9a1a64bd49ab03fa4f738fb250fc4f90","file_name":"2019_DocumMath_Srivastava.pdf","relation":"main_file","access_level":"open_access","file_size":469730,"date_updated":"2020-07-14T12:47:58Z","creator":"dernst","content_type":"application/pdf"}],"file_date_updated":"2020-07-14T12:47:58Z","page":"1135-1177","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Documenta Mathematica","day":"20","publication_status":"published","date_published":"2019-05-20T00:00:00Z","external_id":{"isi":["000517806400019"],"arxiv":["1809.08970"]},"volume":24,"_id":"7436","doi":"10.25537/dm.2019v24.1135-1177","author":[{"first_name":"Tanya K","full_name":"Srivastava, Tanya K","last_name":"Srivastava","id":"4D046628-F248-11E8-B48F-1D18A9856A87"}]}