Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: the Rank Theorem

By Kai-Uwe Bux, Ralf Kohl, Stefan Witzel. 2011

53 citations recorded by the source corpus.

We show that the niteness length of an S-arithmetic subgroup in a noncommutative isotropic absolutely almost simple groupG over a global function eld is one less than the sum of the local ranks of G taken over the places in S. This determines the niteness properties for S-arithmetic subgroups in isotropic reductive groups, conrming the conjectured niteness properties for this class of groups. Our main tool is Behr{Harder reduction theory which we recast in terms of the metric structure of euclidean buildings.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1632bbe62d724e6e2d7274c128137f4e9b6cfb02