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Euler characteristics and their congruences in the positive rank setting

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  11 June 2020

Anwesh Ray  and
R. Sujatha
Anwesh Ray*
Affiliation:
Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY14853-4201, USA
R. Sujatha
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BCV6T 1Z2, Canada e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

The notion of the truncated Euler characteristic for Iwasawa modules is an extension of the notion of the usual Euler characteristic to the case when the homology groups are not finite. This article explores congruence relations between the truncated Euler characteristics for dual Selmer groups of elliptic curves with isomorphic residual representations, over admissible p-adic Lie extensions. Our results extend earlier congruence results from the case of elliptic curves with rank zero to the case of higher rank elliptic curves. The results provide evidence for the p-adic Birch and Swinnerton-Dyer formula without assuming the main conjecture.

Keywords

Iwasawa theory of elliptic curves

MSC classification

Primary: 11R23: Iwasawa theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 228 - 245
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Copyright
© Canadian Mathematical Society 2020

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