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arXiv · 1707.01894

The rank of Mazur's Eisenstein ideal

Preston Wake·Carl Wang-Erickson
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Abstract

We use pseudodeformation theory to study Mazur's Eisenstein ideal. Given prime numbers $N$ and $p>3$, we study the Eisenstein part of the $p$-adic Hecke algebra for $\Gamma_0(N)$. 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.

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BibTeXRIS

Preston Wake, Carl Wang-Erickson. 2017-07-06. The rank of Mazur's Eisenstein ideal. https://doi.org/10.1215/00127094-2019-0039

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