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2008 On the Failure of the Gorenstein Property for Hecke Algebras of Prime Weight
L. J. P. Kilford, Gabor Wiese
Experiment. Math. 17(1): 37-52 (2008).

Abstract

In this article we report on extensive calculations concerning the Gorenstein defect for Hecke algebras of spaces of modular forms of prime weight $p$ at maximal ideals of residue characteristic $p$ such that the attached mod-$p$ Galois representation is unramified at $p$ and the Frobenius at $p$ acts by scalars. The results lead us to ask the question whether the Gorenstein defect and the multiplicity of the attached Galois representation are always equal to $2$. We review the literature on the failure of the Gorenstein property and multiplicity one, discuss in some detail a very important practical improvement of the modular-symbols algorithm over finite fields, and include precise statements on the relationship between the Gorenstein defect and the multiplicity of Galois representations.

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L. J. P. Kilford. Gabor Wiese. "On the Failure of the Gorenstein Property for Hecke Algebras of Prime Weight." Experiment. Math. 17 (1) 37 - 52, 2008.

Information

Published: 2008
First available in Project Euclid: 18 November 2008

zbMATH: 1206.11070
MathSciNet: MR2410114

Subjects:
Primary: 11F80
Secondary: 11F25 , 11F33

Keywords: Gorenstein property , Hecke algebras , mod-$p$ modular forms , Multiplicities of Galois representations

Rights: Copyright © 2008 A K Peters, Ltd.

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Vol.17 • No. 1 • 2008
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