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Kida's formula and congruences

Robert Pollack·Tom Weston
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Abstract

We prove a formula (analogous to that of Kida in classical Iwasawa theory and generalizing that of Hachimori-Matsuno for elliptic curves) giving the analytic and algebraic p-adic Iwasawa invariants of a modular eigenform over an abelian p-extension of Q to its p-adic Iwasawa invariants over Q. On the algebraic side our methods, which make use of congruences between modular forms, yield a Kida-type formula for a very general class of ordinary Galois representations. We are further able to deduce a Kida-type formula for elliptic curves at supersingular primes.

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Robert Pollack, Tom Weston. 2005-08-30. Kida's formula and congruences. https://arxiv.org/abs/math/0508608

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