A Stacky Approach to Crystals

Vladimir Drinfeld ()
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Vladimir Drinfeld: University of Chicago, Department of Mathematics

Chapter Chapter 2 in Dialogues Between Physics and Mathematics, 2022, pp 19-47 from Springer

Abstract: Abstract Inspired by a theorem of Bhatt–Morrow–Scholze, we develop a stacky approach to crystals and isocrystals on “Frobenius-smooth” schemes over 𝔽 p $${\mathbb {F}}_p\,$$ . This class of schemes goes back to Berthelot-Messing and contains all smooth schemes over perfect fields of characteristic p. To treat isocrystals, we prove some descent theorems for sheaves of Banachian modules, which could be interesting in their own right.

Keywords: F-isocrystal; Slope filtration; Tannakian category; Formal group; Semiperfect ring (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-17523-7_2

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DOI: 10.1007/978-3-031-17523-7_2

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