A cohomological obstruction to the Hasse principle for homogeneous spaces
type: Item
instance of: scholarly article
title: A cohomological obstruction to the Hasse principle for homogeneous spaces
zbMATH Open document ID: 0966.14017
author: Mikhail Borovoi
published in: Mathematische Annalen
publication date: 1999-09-14T00:00:00Z
review text: Let \(G\) be a connected algebraic group defined over a number field \(k\), and let \(X\) be a homogeneous space of \(G\) defined over \(k\), whose stabiliser is either connected or Abelian. A few years ago, the author proved [see \textit{M. Borovoi}, J. Reine Angew. Math. 473, 181-194 (1996; Zbl 0844.14020)] that the Brauer-Manin obstruction is the only obstruction to the Hasse principle for \(X\). In this paper, the Brauer-Manin obstruction is computed in terms of the Galois hypercohomology of \(G\) with coefficients in the complex of Abelian \(k\)-groups.
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 11E72
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 11G35
zbMATH DE Number: 1337008
zbMATH Keywords: homogeneous space
zbMATH Keywords: Brauer-Manin obstruction
zbMATH Keywords: Hasse principle
zbMATH Keywords: Galois hypercohomology
reviewed by: B. Z. Moroz
MaRDI profile type: Publication
full work available at URL: s002080050304
OpenAlex ID: W2017892840
DOI: 10.1007/S002080050304
description: scientific article; zbMATH DE number 1337008