On the Ramification of Hecke Algebras at Eisenstein Primes

2003/11/21 by Frank Calegari, Calegari, Frank, Matthew Emerton +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.NT #msc:11F80 #msc:11R29

paper · pdf · doi:10.48550/arxiv.math/0311368

39 pages

arxiv created 2003/11/21 · arxiv updated 2009/12/01

Abstract

Using the modularity technique of Wiles, we study the Hecke algebra of weight 2 and prime level N localized at the Eisenstein primes. On the way, we recover some results of Mazur ("Modular Curves and the Eisenstein Ideal") from a deformation theoretic point of view. Combining some of our results with a theorem of Merel, we obtain new information about the p-part of the class groups of Q(N^(1/p)), where p and N are prime, and N = 1 mod p.

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