Homology of strict polynomial functors over Fp-linear additive categories

Autor:	Djament, Aurélien, Touzé, Antoine
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Topology Mathematics - Category Theory Mathematics - Group Theory Mathematics - K-Theory and Homology Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	We generalize the strong comparison theorem of Franjou, Friedlander, Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in terms of explicit computations of functor homology, and they open the way to new applications to stable homology of groups or to K-theory. As an illustration, we prove comparison theorems between cohomologies of classical algebraic groups over infinite perfect fields, in the spirit of a celebrated result of Cline, Parshall, Scott et van der Kallen for finite fields. Comment: This preprint reworks a part of the material of our previous preprint ''Functor homology over an additive category'' (hal-03432824 or arXiv:2111.09719), which is being completely reorganized. 48 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.10502 Zobrazit plný text záznamu View this record from Arxiv