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arXiv · 2604.03887

Cohomology of special unitary groups and congruence subgroups

Claudio Bravo
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Abstract

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 $\mathrm{PGL}_2(F)$.

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Claudio Bravo. 2026-04-04. Cohomology of special unitary groups and congruence subgroups. https://arxiv.org/abs/2604.03887

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