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, thereby answering a question of Mazur and generalizing a result of Calegari and Emerton. We also give new proofs of Merel’s result on this rank and of Mazur’s results on the structure of the Hecke algebra.
"The rank of Mazur’s Eisenstein ideal." Duke Math. J. 169 (1) 31 - 115, 15 January 2020. https://doi.org/10.1215/00127094-2019-0039