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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Finitude homologique des foncteurs sur une catégorie additive et applications
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by Aurélien Djament and Antoine Touzé PDF
Trans. Amer. Math. Soc. 376 (2023), 1113-1154 Request permission

Abstract:

We give sufficient conditions which ensure that a functor of finite length from an additive category to finite-dimensional vector spaces has a projective resolution whose terms are finitely generated. For polynomial functors, we study also a weaker homological finiteness property, which applies to twisted homological stability for matrix monoids. This is inspired by works by Schwartz and Betley-Pirashvili, which are generalised; this also uses decompositions à la Steinberg over an additive category that we recently obtained with Vespa. We show also, as an application, a finiteness property for stable homology of linear groups on suitable rings.
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Additional Information
  • Aurélien Djament
  • Affiliation: CNRS, Univ. Lille, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France
  • ORCID: 0000-0001-7788-9133
  • Email: aurelien.djament@univ-lille.fr
  • Antoine Touzé
  • Affiliation: Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France
  • ORCID: 0000-0002-9280-6647
  • Email: antoine.touze@univ-lille.fr
  • Received by editor(s): November 19, 2021
  • Received by editor(s) in revised form: May 3, 2022, and May 6, 2022
  • Published electronically: October 24, 2022
  • Additional Notes: Les auteurs ont bénéficié du soutien partiel de l’Agence Nationale de la Recherche, via le projet ANR ChroK (ANR-16-CE40-0003), le Labex CEMPI (ANR-11-LABX-0007-01), et, pour le premier auteur, le projet ANR AlMaRe (ANR-19-CE40-0001-01). Ils ne soutiennent pas pour autant le principe de l’ANR, dont ils revendiquent la restitution des moyens aux laboratoires sous forme de crédits récurrents.

  • Dedicated: Dédié à S. Betley, T. Pirashvili et L. Schwartz pour leurs contributions pionnières au sujet.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 1113-1154
  • MSC (2020): Primary 18A25, 18E10, 18G15, 20J06; Secondary 18A40, 18E05, 18G31
  • DOI: https://doi.org/10.1090/tran/8745
  • MathSciNet review: 4531671