The rank of Mazur's Eisenstein ideal
Number Theory
2020-02-12 v3
Abstract
We use pseudodeformation theory to study Mazur's Eisenstein ideal. Given prime numbers and , we study the Eisenstein part of the -adic Hecke algebra for . We compute the rank of this Hecke algebra (and, more generally, its Newton polygon) in terms of Massey products in Galois cohomology, answering a question of Mazur and generalizing a result of Calegari-Emerton. We also also give new proofs of Merel's result on this rank and of Mazur's results on the structure of the Hecke algebra.
Keywords
Cite
@article{arxiv.1707.01894,
title = {The rank of Mazur's Eisenstein ideal},
author = {Preston Wake and Carl Wang-Erickson},
journal= {arXiv preprint arXiv:1707.01894},
year = {2020}
}
Comments
63 pages. Final version. Improvements to exposition and minor corrections, added dedication. To appear in Duke Math J