A proper base change theorem for non-torsion sheaves in étale cohomology
type: Item
instance of: scholarly article
title: A proper base change theorem for non-torsion sheaves in étale cohomology
zbMATH Open document ID: 0672.14010
DOI: 10.1016/0022-4049(88)90102-8
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: This note extends the proper base change theorem for torsion sheaves to the following. Given noetherian schemes with Y excellent, a proper morphism \(\pi:\quad Y\to X,\) a morphism \(f:\quad X'\to X\) whose pullback \(f':\quad Y'\to Y\) is normal, and an abelian sheaf F on Y, the base change morphisms \(f^*(R^{\bullet}\pi_*F)\to R^{\bullet}(\pi_*'f'{}^*F)\) are isomorphisms. The proof uses the original theorem, standard results on étale cohomology, and results from SGA 4 (Sém. Géométrie algébrique 4).
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 14D99
zbMATH DE Number: 4099464
zbMATH Keywords: proper base change theorem
zbMATH Keywords: étale cohomology
author: Christopher Deninger
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90102-8
OpenAlex ID: W1979164109
Wikidata QID: Q61012318
cites work: Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
cites work: Q5602063
cites work: Values of zeta-functions at non-negative integers
cites work: Q3871006
description: scientific article; zbMATH DE number 4099464