Étale cohomology of Henselian rings and cohomology of abstract Riemann surfaces of fields
type: Item
instance of: scholarly article
title: Étale cohomology of Henselian rings and cohomology of abstract Riemann surfaces of fields
zbMATH Open document ID: 0789.14013
DOI: 10.1007/BF01444911
author: Roland Huber
published in: Mathematische Annalen
publication date: 1994-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/165066
review text: In this short paper, we show that for every ring \(A\) which is henselian along an ideal \(I \subseteq A\), every torsion sheaf \(F\) on the étale site \(\text{Spec} (A)_{et}\) and every \(n \in \mathbb{N}\) the restriction homomorphism \(H^ n(\text{Spec} (A)_{et},F) \to H^ n(\text{Spec} (A/I)_{et},F)\) is bijective. In order to prove this, we show that the cohomology of constant torsion sheaves on certain pro-constructible subsets of abstract Riemann surfaces of algebraically closed fields vanishes.
Mathematics Subject Classification ID: 14F20
Mathematics Subject Classification ID: 13J15
Mathematics Subject Classification ID: 14H55
zbMATH DE Number: 537233
zbMATH Keywords: henselian ring
zbMATH Keywords: étale site
zbMATH Keywords: Riemann surface
reviewed by: Frank Herrlich
MaRDI profile type: Publication
cites work: Q4405003
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OpenAlex ID: W2041662516
description: scientific article; zbMATH DE number 537233