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Class groups and Selmer groups in special families

Part of: Algebraic number theory: local and $p$-adic fields Arithmetic algebraic geometry Algebraic number theory: global fields

Published online by Cambridge University Press:  10 June 2025

Debanjana Kundu  and
Abhishek
Debanjana Kundu
Affiliation:
Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, United States e-mail: debanjana.kundu@utrgv.edu
Abhishek*
Affiliation:
Department of Mathematics and Statistics, IIT Kanpur, Kanpur, India
*
e-mail: abhi.math04@gmail.com
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Abstract

We explore the relationship between (3-isogeny induced) Selmer group of an elliptic curve and the (3 part of) the ideal class group, over certain non-abelian number fields.

Keywords

Elliptic curves3-Selmer groupsideal class groups

MSC classification

Primary: 11G05: Elliptic curves over global fields 11R29: Class numbers, class groups, discriminants 11R34: Galois cohomology
Secondary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11S25: Galois cohomology

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Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 23
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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