Cohomology of special unitary groups and congruence subgroups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918428294512640 |
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| author | Bravo, Claudio |
| author_facet | Bravo, Claudio |
| contents | We prove a homotopy invariance result for the first cohomology group of the special unitary group $\mathrm{SU}_3(F[t])$ with coefficients in irreducible representations of $\mathrm{PGL}_2(F)$. The main theorem establishes that this cohomology is naturally isomorphic to the corresponding cohomology of $\mathrm{PGL}_2(F)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03887 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cohomology of special unitary groups and congruence subgroups Bravo, Claudio K-Theory and Homology Group Theory Number Theory primary 20G10, 20G30, 20H05, secondary 11E57, 14L15 We prove a homotopy invariance result for the first cohomology group of the special unitary group $\mathrm{SU}_3(F[t])$ with coefficients in irreducible representations of $\mathrm{PGL}_2(F)$. The main theorem establishes that this cohomology is naturally isomorphic to the corresponding cohomology of $\mathrm{PGL}_2(F)$. |
| title | Cohomology of special unitary groups and congruence subgroups |
| topic | K-Theory and Homology Group Theory Number Theory primary 20G10, 20G30, 20H05, secondary 11E57, 14L15 |
| url | https://arxiv.org/abs/2604.03887 |