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15 January 2020 The rank of Mazur’s Eisenstein ideal
Preston Wake, Carl Wang-Erickson
Duke Math. J. 169(1): 31-115 (15 January 2020). DOI: 10.1215/00127094-2019-0039

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 Γ0(N). 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.

Citation

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Preston Wake. Carl Wang-Erickson. "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

Information

Received: 29 September 2017; Revised: 15 April 2019; Published: 15 January 2020
First available in Project Euclid: 21 November 2019

zbMATH: 07198455
MathSciNet: MR4047548
Digital Object Identifier: 10.1215/00127094-2019-0039

Subjects:
Primary: 11F80
Secondary: 11F33

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 1 • 15 January 2020
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