Syntomic cohomology and \(p\)-adic étale cohomology
type: Item
instance of: scholarly article
title: Syntomic cohomology and \(p\)-adic étale cohomology
zbMATH Open document ID: 0792.14008
author: Kazuya Kato
author: William Messing
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-07-25T00:00:00Z
review text: This article is a complement to the paper ``\(p\)-adic periods and \(p\)-adic étale cohomology'' by \textit{J.-M. Fontaine} and \textit{W. Messing} [in Current trends in arithmetical algebraic geometry, Proc. Summer Res. Conf., Arcata 1985, Contemp. Math. 67, 179-207 (1987; Zbl 0632.14016)] concerning the \(p\)-adic étale cohomology of varieties over \(p\)-adic fields. In that paper, the absolute ramification index of the base \(p\)- adic field was assumed to be one in the main results. We are interested in composing the method in the paper cited above and the study of \(p\)- adic vanishing cycles in the paper by \textit{S. Bloch} and \textit{K. Kato} [Publ. Math., Inst. Hautes Étud. Sci. 63, 107-152 (1986; Zbl 0613.14017)]. We show that the composition gives, for a smooth proper variety with good reduction over a \(p\)-adic field and whose dimension not too big, fairly short proofs of the Hodge-Tate decomposition and of the crystalline conjecture without the assumption on the absolute ramification index. The Hodge-Tate decomposition and the crystalline conjecture were proved by Faltings without any assumption. The aim of this paper is to show the existence of a different method.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 14G20
zbMATH DE Number: 570298
zbMATH Keywords: \(p\)-adic étale cohomology
zbMATH Keywords: \(p\)-adic vanishing cycles
zbMATH Keywords: Hodge-Tate decomposition
zbMATH Keywords: crystalline conjecture
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227370
OpenAlex ID: W1965139297
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DOI: 10.2748/TMJ/1178227370
description: scientific article; zbMATH DE number 570298