Homology of strict polynomial functors over Fp-linear additive categories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929421177323520 |
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| author | Djament, Aurélien Touzé, Antoine |
| author_facet | Djament, Aurélien Touzé, Antoine |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_10502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homology of strict polynomial functors over Fp-linear additive categories Djament, Aurélien Touzé, Antoine Algebraic Topology Category Theory Group Theory K-Theory and Homology Representation Theory 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. |
| title | Homology of strict polynomial functors over Fp-linear additive categories |
| topic | Algebraic Topology Category Theory Group Theory K-Theory and Homology Representation Theory |
| url | https://arxiv.org/abs/2407.10502 |