Finitude homologique des foncteurs sur une catégorie additive et applications
| Autor: | Aurélien Djament, Antoine Touzé |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Transactions of the American Mathematical Society. |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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