K-theory of rank one reductive p-adic groups and Bernstein blocks
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909263445622784 |
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| author | Tönies, Maximilian |
| author_facet | Tönies, Maximilian |
| contents | We prove a colimit formula for the K-theory spectra of reductive p-adic groups of rank one with regular coefficients in terms of the K-theory of certain compact open subgroups. Furthermore, in the complex case, we show, using the construction of types provided by Roche, that this result can be improved to obtain a formula for the K-theory spectrum of every principal series Bernstein block if the group is split. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-theory of rank one reductive p-adic groups and Bernstein blocks Tönies, Maximilian K-Theory and Homology We prove a colimit formula for the K-theory spectra of reductive p-adic groups of rank one with regular coefficients in terms of the K-theory of certain compact open subgroups. Furthermore, in the complex case, we show, using the construction of types provided by Roche, that this result can be improved to obtain a formula for the K-theory spectrum of every principal series Bernstein block if the group is split. |
| title | K-theory of rank one reductive p-adic groups and Bernstein blocks |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2407.14929 |