On the top-dimensional cohomology of arithmetic Chevalley groups
journal contribution
posted on 2024-07-23, 13:45 authored by Benjamin Brück, Yuri Santos RegoYuri Santos Rego, Robin SrokaAbstract:
Let 𝕂 be a number field with ring of integers 𝔒 and let 𝒢 be a Chevalley group scheme not of type 𝙴8, 𝙵4 or 𝙶2. We use the theory of Tits buildings and a result of Tóth on Steinberg modules to prove that 𝐻vcd(𝒢(𝔒);ℚ)=0 if 𝔒 is Euclidean.
Funding
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 427320536 – SFB 1442
Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Priority Programme SPP2026 'Geometry at Infinity', Project 62
Germany’s Excellence Strategy EXC 2044 – 390685587, Mathematics Münster: Dynamics–Geometry–Structure
European Research Council (ERC grant agreement No.772960)
Danish National Research Foundation (DNRF92, DNRF151)
NSERC Discovery Grant A4000
History
School affiliated with
- School of Mathematics and Physics (Research Outputs)
- College of Health and Science (Research Outputs)
Publication Title
Proceedings of the American Mathematical SocietyVolume
152Pages/Article Number
4131-4139Publisher
American Mathematical SocietyExternal DOI
ISSN
0002-9939eISSN
1088-6826Date Accepted
2024-04-30Date of First Publication
2024-08-26Date of Final Publication
2024-08-26Open Access Status
- Not Open Access
