Mathematics > Number Theory
[Submitted on 12 Dec 2018 (v1), last revised 11 Jul 2021 (this version, v3)]
Title:A crystalline incarnation of Berthelot's conjecture and Künneth formula for isocrystals
View PDFAbstract:Berthelot's conjecture predicts that under a proper and smooth morphism of schemes in characteristic $p$, the higher direct images of an overconvergent $F$-isocrystal are overconvergent $F$-isocrystals. In this paper we prove that this is true for crystals up to isogeny. As an application we prove a Künneth formula for the crystalline fundamental group.
Submission history
From: Lei Zhang [view email][v1] Wed, 12 Dec 2018 20:44:29 UTC (43 KB)
[v2] Tue, 3 Nov 2020 20:13:30 UTC (53 KB)
[v3] Sun, 11 Jul 2021 09:32:11 UTC (73 KB)
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