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Sur la noethérianité locale des foncteurs polynomiaux

Aurélien Djament and Antoine Touzé

Vol. 6 (2024), No. 1, 97–113
Abstract

Soient A un anneau commutatif de type fini et k un anneau commutatif noethérien. On montre que, dans la catégorie des foncteurs des A-modules projectifs de type fini vers les k-modules, tout foncteur polynomial de type fini est noethérien et possède une résolution projective de type fini.

Let A be a finitely generated commutative ring and k a noetherian commutative ring. We show that, in the category of functors from finitely generated projective A-modules to k-modules, each finitely generated polynomial functor is noetherian and has a finitely generated projective resolution.

Keywords
polynomial functors, strict polynomial functors, noetherianity, finitely generated projective resolutions
Mathematical Subject Classification
Primary: 16P40, 18A25, 18E05, 18G10, 20G43
Milestones
Received: 29 November 2022
Revised: 30 May 2023
Accepted: 18 June 2023
Published: 20 January 2024
Authors
Aurélien Djament
LAGA (UMR 7539)
CNRS
Institut Galilée
Villetaneuse
France
Antoine Touzé
Laboratoire Paul Painlevé (UMR 8524)
Faculté des Sciences et Technologies
Université de Lille
Villeneuve-d’Ascq
France