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Level 1 Hecke algebras of modular forms modulo $p$

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  27 November 2014

Joël Bellaïche  and
Chandrashekhar Khare
Joël Bellaïche
Affiliation:
Mathematics Department, Brandeis University, 415 South Street, Waltham, MA 02454-9110, USA email jbellaic@brandeis.edu
Chandrashekhar Khare
Affiliation:
Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095-1555, USA email shekhar@math.ucla.edu
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Abstract

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In this paper, we study the structure of the local components of the (shallow, i.e. without $U_{p}$) Hecke algebras acting on the space of modular forms modulo $p$ of level $1$, and relate them to pseudo-deformation rings. In many cases, we prove that those local components are regular complete local algebras of dimension $2$, generalizing a recent result of Nicolas and Serre for the case $p=2$.

Keywords

modular forms modulo pHecke algebrasdeformation of Galois representations

MSC classification

Primary: 11F25: Hecke-Petersson operators, differential operators (one variable) 11F33: Congruences for modular and $p$-adic modular forms 11F80: Galois representations
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 3 , March 2015 , pp. 397 - 415
Copyright
© The Author(s) 2014 

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