On the divisibility properties of families of filtered F-crystals
type: Item
instance of: scholarly article
title: On the divisibility properties of families of filtered F-crystals
zbMATH Open document ID: 0692.14010
DOI: 10.1007/BF01444539
author: Adolfo Quirós
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164741
review text: Let \(V\) be a complete discrete valuation ring of unequal characteristic, with perfect residue field k and fraction field \(K\). Let \(W\) be the ring of Witt vectors over \(k\). We study the divisibility properties, with respect to the actionof Frobenius, of families of filtered F-crystals over a smooth formal \(W\)-scheme, and apply these to study the weak admissibility (in the sense of Fontaine) of the fibres. We use the results to give conditions under which the de Rham cohomology of a proper and smooth scheme over \(K\) with good reduction is weakly admissible.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 13K05
Mathematics Subject Classification ID: 13A35
zbMATH DE Number: 4132325
zbMATH Keywords: Hodge filtration
zbMATH Keywords: Gauss-Manin connection
zbMATH Keywords: crystalline cohomology
zbMATH Keywords: de Rham cohomology
zbMATH Keywords: Witt vectors
zbMATH Keywords: divisibility
zbMATH Keywords: action of Frobenius
zbMATH Keywords: filtered F- crystals
MaRDI profile type: Publication
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OpenAlex ID: W359249433
description: scientific article; zbMATH DE number 4132325