Potential semi-stability of \(p\)-adic étale cohomology
type: Item
instance of: scholarly article
title: Potential semi-stability of \(p\)-adic étale cohomology
zbMATH Open document ID: 0999.14005
DOI: 10.1007/BF02773161
author: Mark Kisin
published in: Israel Journal of Mathematics
publication date: 2002-08-22T00:00:00Z
review text: The paper under review shows that for an arbitrary scheme \(X\) of finite type over a \(p\)-adic field \(K\) (completely discretely valued of characteristic zero, with perfect residue-field of characteristic \(p\)) the \(p\)-adic étale cohomology is potentially semistable, that is after a finite extension of \(K\) it is associated (in the sense of Fontaine's functors) to a suitable crystalline object. Previously this had been shown for proper smooth schemes, and the essential idea is to reduce to that case using simplicial techniques, just as it is done in complex Hodge theory. However this makes it necessary to repeat certain local arguments in this context, to first construct a map between étale and crystalline cohomology, and there are also a number of subtleties one has to take care of. One other important ingredient of the proof is of course de Jong's reduction theory which allows to assume semistable reduction.
Mathematics Subject Classification ID: 14F30
zbMATH DE Number: 1760713
zbMATH Keywords: crystalline cohomology
zbMATH Keywords: Fontaine theory
MaRDI profile type: Publication
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reviewed by: Gerd Faltings
description: scientific article; zbMATH DE number 1760713