On the Ramification of Hecke Algebras at Eisenstein Primes

Details On the Ramification of Hecke Algebras at Eisenstein Primes On the Ramification of Hecke Algebras at Eisenstein Primes

2003-11-21

arxiv.org/abs/math/0311368v1

Mathematics

Number Theory

39 pages

Scientific paper

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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