2016/09/27 by Matthias Wendt, Wendt, Matthias
Mathematics · #20E42) #20G10 (11F75 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:20G10
paper · pdf · doi:10.48550/arxiv.1609.08278
50 pages, comments very welcome!
arxiv created 2016/09/27 · openalex publication_date 2016/09/27 · arxiv updated 2016/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper provides a computation of the additive structure as well as a partial description of the Chern-class module structure of the cohomology of GL3 over the function ring of an elliptic curve over a finite field. The computation is achieved by a detailed analysis of the isotropy spectral sequence for the action of GL3 on the associated Bruhat-Tits building. This provides insights into the function field version of Quillen's conjecture on the structure of cohomology rings of arithmetic groups. The computations exhibit a lot of explicit classes which are torsion for the Chern-class ring. In some examples, even the torsion-free quotient of cohomology fails to be free. A possible variation of Quillen's conjecture is also discussed.