F-isocrystals and de Rham cohomology. II: Convergent isocrystals
type: Item
instance of: scholarly article
title: F-isocrystals and de Rham cohomology. II: Convergent isocrystals
zbMATH Open document ID: 0584.14008
DOI: 10.1215/S0012-7094-84-05136-6
author: Arthur Ogus
published in: Duke Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: [For part I see \textit{P. Berthelot} and the author, Invent. Math. 72, 159- 199 (1983; Zbl 0516.14017).] The author studies the relation between de Rham and crystalline cohomology for a smooth proper map of flat V-schemes (V a complete discrete valuation ring with fraction field of characteristic 0 and residue field of characteristic \(p>0).\) For this the notion of convergent isocrystal (a collection of sheaves on certain ''thickenings'' of schemes over \({\mathbb{Z}})\) is introduced and used to study p-adic analytic continuation. The main application shows the compatibility of the absolute Hodge cycle linking a K3 surface to its Kuga-Satake abelian variety with the action of Frobenius on crystalline cohomology.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14D99
zbMATH DE Number: 3935197
zbMATH Keywords: de Rham cohomology
zbMATH Keywords: crystalline cohomology
zbMATH Keywords: discrete valuation ring
zbMATH Keywords: convergent isocrystal
zbMATH Keywords: p-adic analytic continuation
zbMATH Keywords: absolute Hodge cycle
zbMATH Keywords: K3 surface
zbMATH Keywords: Kuga-Satake abelian variety
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3935197