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Relative homology of arithmetic subgroups of SU(3)

  • Claudio Bravo
Published/Copyright: July 10, 2024

Abstract

Let 𝑘 be a global field of positive characteristic. Let G = SU ⁹ ( 3 ) be the non-split group scheme defined from an (isotropic) hermitian form in three variables. In this work, we describe, in terms of the Euler–PoincarĂ© characteristic, the relative homology groups of certain arithmetic subgroups đș of G ⁹ ( k ) modulo a representative system 𝔘 of the conjugacy classes of their maximal unipotent subgroups. In other words, we measure how far the homology groups of đș are from being the coproducts of the corresponding homology groups of the subgroups U ∈ U .

Award Identifier / Grant number: 74220027

Funding statement: I express my gratitude to Anid-Conicyt for the postdoctoral fellowship [74220027].

Acknowledgements

I would like to thank the anonymous referee for helpful comments.

  1. Communicated by: Rachel Skipper

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Received: 2023-09-09
Revised: 2024-06-03
Published Online: 2024-07-10
Published in Print: 2025-01-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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