Kida's formula and congruences
数论
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0508608,
title = {Kida's formula and congruences},
author = {Robert Pollack and Tom Weston},
journal= {arXiv preprint arXiv:math/0508608},
year = {2007}
}