Iwasawa Invariants for elliptic curves over $\mathbb{Z}_{p}$-extensions and Kida's Formula
Debanjana Kundu,
Anwesh Ray
Abstract:This paper aims at studying the Iwasawa λ-invariant of the p-primary Selmer group. We study the growth behaviour of p-primary Selmer groups in p-power degree extensions over non-cyclotomic Zp-extensions of a number field. We prove a generalization of Kida's formula in such a case. Unlike the cyclotomic Zp-extension, where all primes are finitely decomposed; in the Zp-extensions we consider, primes may be infinitely decomposed. In the second part of the paper, we study the relationship for Iwasawa invariants wi… Show more
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