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.
Publié le : 2008-05-15
Classification:
Multiplicities of Galois representations,
Gorenstein property,
Hecke algebras,
mod-$p$ modular forms,
11F80,
11F33,
11F25
@article{1227031895,
author = {Kilford, L. J. P. and Wiese, Gabor},
title = {On the Failure of the Gorenstein Property for Hecke Algebras of Prime Weight},
journal = {Experiment. Math.},
volume = {17},
number = {1},
year = {2008},
pages = { 37-52},
language = {en},
url = {http://dml.mathdoc.fr/item/1227031895}
}
Kilford, L. J. P.; Wiese, Gabor. On the Failure of the Gorenstein Property for Hecke Algebras of Prime Weight. Experiment. Math., Tome 17 (2008) no. 1, pp. 37-52. http://gdmltest.u-ga.fr/item/1227031895/