Arithmetic properties of three-dimensional algebraic tori
type: Item
instance of: scholarly article
title: Arithmetic properties of three-dimensional algebraic tori
zbMATH Open document ID: 0556.14020
DOI: 10.1007/BF01670577
published in: Journal of Soviet Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let K/k be an extension of degree 4 of an algebraic number field with the Galois group of its normal closure isomorphic to either alternating group \(A_ 4\) or \({\mathbb{Z}}/2\oplus {\mathbb{Z}}/2\). The author studies some arithmetical properties of 3-dimensional algebraic tori over k which are obtained as the kernel of the norm map \(N_{K/k}: R_{K/k}(G_ m)\to G_ m,\) where \(R_{K/k}\) is the Weil restriction functor. In particular, the author verifies for these tori the Hasse principle and the property of weak specialization.
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14L40
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 14G25
zbMATH DE Number: 3886047
zbMATH Keywords: 3-dimensional algebraic tori
zbMATH Keywords: Weil restriction functor
zbMATH Keywords: Hasse principle
author: Boris Kunyavskiĭ
reviewed by: Igor V. Dolgachev
MaRDI profile type: Publication
cites work: On the Tamagawa number of algebraic tori
cites work: Q5612630
cites work: Q3904704
cites work: The Hasse norm principle in non-abelian extensions.
full work available at URL: https://doi.org/10.1007/bf01670577
OpenAlex ID: W2060761801
description: scientific article; zbMATH DE number 3886047