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Abstract
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Soient
un anneau
commutatif de type fini et
un anneau commutatif noethérien. On montre que, dans la catégorie des foncteurs des
-modules projectifs de
type fini vers les
-modules,
tout foncteur polynomial de type fini est noethérien et possède une résolution
projective de type fini.
Let
be a finitely generated
commutative ring and
a noetherian commutative ring. We show that, in the category of functors from finitely generated
projective
-modules
to
-modules,
each finitely generated polynomial functor is noetherian and has a finitely generated
projective resolution.
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Keywords
polynomial functors, strict polynomial functors,
noetherianity, finitely generated projective resolutions
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Mathematical Subject Classification
Primary: 16P40, 18A25, 18E05, 18G10, 20G43
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Milestones
Received: 29 November 2022
Revised: 30 May 2023
Accepted: 18 June 2023
Published: 20 January 2024
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© 2024 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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