--- res: bibo_abstract: - 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. @eng bibo_authorlist: - foaf_Person: foaf_givenName: Tanya K foaf_name: Srivastava, Tanya K foaf_surname: Srivastava foaf_workInfoHomepage: http://www.librecat.org/personId=4D046628-F248-11E8-B48F-1D18A9856A87 bibo_doi: 10.25537/dm.2019v24.1135-1177 bibo_volume: 24 dct_date: 2019^xs_gYear dct_identifier: - UT:000517806400019 dct_isPartOf: - http://id.crossref.org/issn/1431-0635 - http://id.crossref.org/issn/1431-0643 dct_language: eng dct_publisher: EMS Press@ dct_title: On derived equivalences of k3 surfaces in positive characteristic@ ...