On the Hasse principle for homogeneous spaces with finite stabilizers
type: Item
instance of: scholarly article
title: On the Hasse principle for homogeneous spaces with finite stabilizers
zbMATH Open document ID: 0905.14012
author: Mikhail Borovoi
author: Boris Kunyavskiĭ
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1999-02-04T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73429
review text: Let \(X\) be an algebraic variety over a number field \(k\). The variety \(X\) is called a counter example to the Hasse principle if \(X\) has a \(k_v\)-point for any completion \(k_v\) of \(k\) but has no \(k\)-points. \textit{Yu. I. Manin} [in: Actes Congr. Int. Math., Nice 1970, No. 1, 401-411 (1971; Zbl 0239.14010) and in his book: ``Cubic Forms: Algebra, Geometry, Arithmetic'' (1972; Zbl 0255.14002; see also the English translation thereof: 1974; Zbl 0277.14014)] proposed a general method of obtaining obstructions to the Hasse principle with the use of the Brauer group of \(X\). Manin's method gives an obstruction for \(X\) to have a \(k\)-point. The authors of this paper give another counter example to the Hasse principle.
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14G05
zbMATH DE Number: 1139506
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: obstructions to the Hasse principle
zbMATH Keywords: Brauer group
MaRDI profile type: Publication
OpenAlex ID: W2021418639
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DOI: 10.5802/AFST.874
description: scientific article; zbMATH DE number 1139506