A note on the Bloch-Tamagawa space and Selmer groups

DOI10.3792/PJAA.91.61zbMATH Open1378.11072arXiv1501.00640OpenAlexW2954259914MaRDI QIDQ498684

Niranjan Ramachandran

Publication date: 29 September 2015

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Abstract: For any abelian variety $A$ over a number field, we construct an extension of the Tate-Shafarevich group by the Bloch-Tamagawa space using the recent work of Lichtenbaum and Flach. This gives a new example of a Zagier sequence for the Selmer group of $A$.

Full work available at URL: https://arxiv.org/abs/1501.00640

zbMATH Keywords

\(L\)-functionsabelian varietiesSelmer groupsTamagawa numbers

Mathematics Subject Classification ID

Linear algebraic groups over global fields and their integers (20G30) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Arithmetic ground fields for abelian varieties (14K15)

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