On unramified Brauer groups of torsors over tori

DOI10.25537/dm.2020v25.1263-1284zbMath1505.11096arXiv2004.08850MaRDI QIDQ2204343

Raman Parimala, Eva Bayer-Fluckiger

Publication date: 15 October 2020

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.08850

zbMATH Keywords

unramified Brauer groupsTate-Shafarevich groupsnorm toriHasse principle and weak approximation

Mathematics Subject Classification ID

Galois cohomology (12G05) Rational points (14G05) Varieties over global fields (11G35) Global ground fields in algebraic geometry (14G25) Galois cohomology (11R34)

Related Items (1)

The Tate-Shafarevich groups of multinorm-one tori

Cites Work

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• On algebraic tori of norm type
• Principal homogeneous spaces under flasque tori; applications
• The multinorm principle for linearly disjoint Galois extensions
• Purity for the Brauer group
• Hasse principles for multinorm equations
• Unramified Brauer group of homogeneous spaces of tori
• Equivariant compactification of a torus (after Brylinski and Künnemann)
• The norm function of an algebraic field extension
• Lois de réciprocité supérieures et points rationnels
• On non‐ramified extensions with prescribed Galois group
• Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres.
• La $R$-équivalence sur les tores

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