Finitude homologique des foncteurs sur une catégorie additive et applications

Djament, Aurélien; Touzé, Antoine

doi:10.1090/tran/8745

Finitude homologique des foncteurs sur une catégorie additive et applications
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by Aurélien Djament and Antoine Touzé;

Trans. Amer. Math. Soc. 376 (2023), 1113-1154

DOI: https://doi.org/10.1090/tran/8745

Published electronically: October 24, 2022

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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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