Finiteness properties of certain arithmetic groups in the function field case

DOI10.1007/BF02782847zbMath0819.20051MaRDI QIDQ1196328

Herbert Abels

Publication date: 9 December 1992

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

finitely generated groupsprojective resolutionsreductive algebraic groupsglobal function fieldsfinitely presented groupsBruhat-Tits buildingsarithmetic subgroupscellular action of groupsfiniteness length

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generators, relations, and presentations of groups (20F05) Homological methods in group theory (20J05) Linear algebraic groups over global fields and their integers (20G30) Groups with a (BN)-pair; buildings (20E42)

Related Items

Finiteness properties of Chevalley groups over \(\mathbb{F}_ q[t\)] ⋮ Linear groups over general rings. I: Generalities. ⋮ Finiteness properties of arithmetic groups over function fields. ⋮ Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem. ⋮ Spherical subcomplexes of spherical buildings ⋮ Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups. ⋮ Quasi-isometric rigidity of higher rank \(S\)-arithmetic lattices. ⋮ The sphericity of the Phan geometries of type $B_n$ and $C_n$ and the Phan-type theorem of type $F_4$ ⋮ Affine twin \(\mathbb R\)-buildings ⋮ Opposition in triality ⋮ An infinitely generated virtual cohomology group for noncocompact arithmetic groups over function fields.

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