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Iwasawa invariants for elliptic curves over ℤp-extensions and Kida's formula

  • Debanjana Kundu ORCID logo EMAIL logo and Anwesh Ray ORCID logo
From the journal Forum Mathematicum

Abstract

This paper aims at studying the Iwasawa λ-invariant of the p-primary Selmer group. We study the growth behavior of p-primary Selmer groups in p-power degree extensions over non-cyclotomic p-extensions of a number field. We prove a generalization of Kida’s formula in such a case. Unlike the cyclotomic p-extension, where all primes are finitely decomposed, in the p-extensions we consider primes may be infinitely decomposed. In the second part of this paper, we study the relationship of Iwasawa invariants with respect to congruences, obtaining refinements of the results of Greenberg, Vatsal and Kidwell. As an application, we provide an algorithm for constructing elliptic curves with large anticyclotomic λ-invariant. Our results are illustrated by explicit computation.

MSC 2010: 11R23

Communicated by Jan Bruinier


Acknowledgements

The first-named author acknowledges the support of the PIMS Postdoctoral Fellowship. We thank the referee for carefully reading our manuscript.

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Received: 2021-08-05
Revised: 2022-02-24
Published Online: 2022-04-20
Published in Print: 2022-07-01

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