A formula for the S-class number of an algebraic torus

DOI10.1016/j.jnt.2017.06.010zbMath1406.11110arXiv1611.01718OpenAlexW2963573722MaRDI QIDQ2403266

Minh-Hoang Tran

Publication date: 8 September 2017

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.01718

zbMATH Keywords

Galois cohomologyclass number formulaalgebraic torusArtin-Verdier dualityÉtale cohomology

Mathematics Subject Classification ID

Galois theory (11R32) Étale and other Grothendieck topologies and (co)homologies (14F20) Class field theory (11R37) Varieties over global fields (11G35)

Related Items (2)

CLASS NUMBERS OF CM ALGEBRAIC TORI, CM ABELIAN VARIETIES AND COMPONENTS OF UNITARY SHIMURA VARIETIES ⋮ On Tamagawa numbers of CM tori

Cites Work

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• Chevalley's ambiguous class number formula for an arbitrary torus
• On some class number relations of algebraic tori
• Isogenous tori and the class number formulae
• Arithmetic of algebraic tori
• On the Tamagawa number of algebraic tori
• On Néron-Raynaud class groups of tori and the capitulation problem
• On S-class number relations of algebraic tori in Galois extensions of global fields
• The scheme of connected components of the Néron model of an algebraic torus.
• A.D. Alexandrov spaces with curvature bounded below
• On some class number relations for Galois extensions

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