Unramified cohomology and rationality problems
type: Item
instance of: scholarly article
title: Unramified cohomology and rationality problems
zbMATH Open document ID: 0790.12001
DOI: 10.1007/BF01445105
author: Emmanuel Peyre
published in: Mathematische Annalen
publication date: 1994-07-03T00:00:00Z
full work available at URL: https://eudml.org/doc/165085
review text: The aim of this paper is to construct unirational function fields \(K\) over an algebraically closed field of characteristic \(0\) such that the unramified cohomology group \(H^ i_{nr}(K,\mu^{\otimes i}_ p)\neq \{0\}\) for \(i=2,3\) or \(4\) and \(p\) a prime number. This implies that the field \(K\) is not stably rational. For this purpose, a sufficient condition for an element to be unramified in \(H^ i(K,\mu^{\otimes i}_ p)\) is given. This condition relies on computations in the exterior algebra of a vector space of finite dimension over the field \(\mathbb{F}_ p\).
Mathematics Subject Classification ID: 12G05
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 11E72
zbMATH DE Number: 537297
zbMATH Keywords: unirational function fields
zbMATH Keywords: unramified cohomology group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 537297