Reference : On the failure of the Gorenstein property for Hecke algebras of prime weight
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
On the failure of the Gorenstein property for Hecke algebras of prime weight
Kilford, L. J. P. [> >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Experimental Mathematics
Yes (verified by ORBilu)
[en] 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 the ask the question whether the Gorenstein defect and the multplicity 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. The Magma package, instructions for its use, generated tables and the complete data are available as supplemental material.

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nongorenstein.pdfAuthor preprint253.81 kBView/Open

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data.tar.gzComputational data14.86 kBView/Open
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Example.mgMagma example1.26 kBView/Open
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HeckeAlgebra.mgMagma package50.49 kBView/Open
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Manual.pdfManual of Magma package103.96 kBView/Open
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Tables.pdfTables of Hecke algebras102.86 kBView/Open

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