On cohomological dimensions of totally disconnected locally compact groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908774432768000 |
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| author | Castellano, Ilaria Mazza, Nadia Nucinkis, Brita |
| author_facet | Castellano, Ilaria Mazza, Nadia Nucinkis, Brita |
| contents | In this paper, we introduce Mackey functors for a t.d.l.c. group and define the cohomological dimension of this group over the Mackey category. We then compare this dimension to the rational discrete cohomological dimension defined by Castellano and Weigel, as well as to the Bredon cohomological dimension of that t.d.l.c. group with respect to the family of compact open subgroups. We also extend results about the geometric dimension of a t.d.l.c. group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12958 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On cohomological dimensions of totally disconnected locally compact groups Castellano, Ilaria Mazza, Nadia Nucinkis, Brita Group Theory 20J05, 20J06, 22D05, 57T99, 18G In this paper, we introduce Mackey functors for a t.d.l.c. group and define the cohomological dimension of this group over the Mackey category. We then compare this dimension to the rational discrete cohomological dimension defined by Castellano and Weigel, as well as to the Bredon cohomological dimension of that t.d.l.c. group with respect to the family of compact open subgroups. We also extend results about the geometric dimension of a t.d.l.c. group. |
| title | On cohomological dimensions of totally disconnected locally compact groups |
| topic | Group Theory 20J05, 20J06, 22D05, 57T99, 18G |
| url | https://arxiv.org/abs/2601.12958 |