Structure of Hecke algebras of modular forms modulo p

Deo, Shaunak

doi:10.2140/ant.2017.11.1

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Structure of Hecke algebras of modular forms modulo $p$

Shaunak V. Deo

Vol. 11 (2017), No. 1, 1–38

DOI: 10.2140/ant.2017.11.1

Abstract

Generalizing the recent results of Bellaïche and Khare for the level- $1$ case, we study the structure of the local components of the shallow Hecke algebras (i.e., Hecke algebras without $U_{p}$ and $U_{ℓ}$ for all primes $ℓ$ dividing the level $N$ ) acting on the space of modular forms modulo $p$ for $Γ_{0} (N)$ and $Γ_{1} (N)$ . We relate them to pseudodeformation rings and prove that in many cases, the local components are regular complete local algebras of dimension $2$ .

Keywords

Modular forms modulo $p$, Hecke algebras, deformations of Galois representations

Mathematical Subject Classification 2010

Primary: 11F80

Secondary: 11F25, 11F33

Milestones

Received: 31 July 2015

Revised: 5 August 2016

Accepted: 17 November 2016

Published: 23 January 2017

Authors

Shaunak V. Deo
Department of Mathematics MS 050, Brandeis University 415 South Street Waltham, MA 02453 United States	Mathematics Research Unit Université du Luxembourg Faculté des Sciences, de la Technologie et de la Communication 6, rue Richard Coudenhove-Kalergi L-1359 Luxembourg Luxembourg

Vol. 11, No. 1, 2017