Cohomological descent of rigid cohomology for proper coverings
type: Item
instance of: scholarly article
title: Cohomological descent of rigid cohomology for proper coverings
zbMATH Open document ID: 1085.14019
author: Nobuo Tsuzuki
published in: Inventiones Mathematicae
publication date: 2003-08-17T00:00:00Z
review text: This paper is Tsuzuki's ingenious proof of descent for proper coverings of the rigid cohomology of Berthelot. In classical (complex) Hodge theory, cohomological descent of singular cohomology is combined with resolution of singularities to give meaning to mixed Hodge structure on the singular cohomology of a possible singular variety. Similarly, the result of Tsuzuki can be used in combination with \textit{A. J. de Jong}'s alterations [Publ. Math., Inst. Hautes Étud. Sci. 83, 51--93 (1996; Zbl 0916.14005)] to prove that rigid cohomology of a separated scheme of finite type over a field of positive characteristic has bijective Frobenius and is finite dimensional (this was also proven by \textit{E. Grosse-Klönne} [Duke Math. J. 113, No. 1, 57--91 (2002; Zbl 1057.14023)] by a different method). That is just one of the applications.
reviewed by: Gunther Cornelissen
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 14G22
zbMATH DE Number: 1965459
zbMATH Keywords: rigid analysis
zbMATH Keywords: rigid cohomology
zbMATH Keywords: descent
MaRDI profile type: Publication
full work available at URL: s00222-002-0252-9
OpenAlex ID: W2020947103
DOI: 10.1007/S00222-002-0252-9
description: scientific article; zbMATH DE number 1965459