Wiles Defect for Modules and Criteria for Freeness

Sylvain Brochard; Srikanth Iyengar; Chandrashekhar Khare

doi:10.1093/imrn/rnac052

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Wiles Defect for Modules and Criteria for Freeness

Sylvain Brochard, Srikanth Iyengar et Chandrashekhar Khare

International Mathematics Research Notices, Vol.2023(8), pp.6901-6923

25/03/2022

DOI: https://doi.org/10.1093/imrn/rnac052

Résumé

congruence module

freeness criterion

Gorenstein ring

Wiles defect

2020 Mathematics Subject Classification. 11F80 (primary); 13C99, 13F99 (secondary)

Diamond proved a numerical criterion for modules over local rings to be free modules over complete intersection rings. We formulate a refinement of these results using the notion of Wiles defect. A key step in the proof is a formula that expresses the Wiles defect of a module in terms of the Wiles defect of the underlying ring.

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Titre: Wiles Defect for Modules and Criteria for Freeness
Créateurs - sans rôle: Sylvain Brochard - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Srikanth Iyengar - University of Utah
Chandrashekhar Khare - University of California, Los Angeles
Détails de publication: International Mathematics Research Notices, Vol.2023(8), pp.6901-6923
Identifiants: 99161275209311
Unité académique: Institut Montpelliérain Alexander Grothendieck - IMAG
Langue: English
Type de ressource: Journal article
Champs locaux: hal-03643331