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arXiv · 1812.05153

A crystalline incarnation of Berthelot's conjecture and K\"unneth formula for isocrystals

Valentina Di Proietto·Fabio Tonini·Lei Zhang
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Abstract

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 K\"unneth formula for the crystalline fundamental group.

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Valentina Di Proietto, Fabio Tonini, Lei Zhang. 2018-12-12. A crystalline incarnation of Berthelot's conjecture and K\"unneth formula for isocrystals. https://doi.org/10.1090/jag%2F789

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