2005/08/30 by Robert Pollack, Pollack, Robert, Tom Weston +1 · 1 citation
Mathematics · #11F33 #11F80 #11R23 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F33 #msc:11F80 #msc:11R23
paper · pdf · doi:10.48550/arxiv.math/0508608
arxiv created 2005/08/30 · openalex publication_date 2005/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.