On a theorem of Grothendieck
type: Item
instance of: scholarly article
title: On a theorem of Grothendieck
zbMATH Open document ID: 1070.14022
DOI: 10.1023/A:1023471214286
author: Ivan Panin
author: A. L. Smirnov
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-06-08T00:00:00Z
review text: The authors prove the following analog of the result of A. Grothendieck on the cohomology of a coherent sheaf. Theorem. Let \(U\) be a local regular scheme of geometric type over a field \(k\) and \(T\to U\) be a smooth proper morphism. Let \(F\) be a locally constant constructible torsion étale sheaf on \(T\) with torsion prime to characteristic of \(k\). Then there exists a finite complex \(L\) of locally constant constructible sheaves on \(U\) and a functor isomorphism between étale hypercohomology \(H_{\text{ét}}^q(T\times_U U',F) \cong H_{\text{ét}}^q(U',L\times_U U')\), where \(q\geq 0\) and \(U'\) denotes an \(U\)-scheme.
reviewed by: Kirill Zainoulline
Mathematics Subject Classification ID: 14F20
zbMATH DE Number: 2174358
zbMATH Keywords: constructible étale sheaf
zbMATH Keywords: smooth proper base change
MaRDI profile type: Publication
full work available at URL: a:1023471214286
OpenAlex ID: W1584102259
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description: scientific article; zbMATH DE number 2174358