Finiteness Properties of Arithmetic Groups Acting on Twin Buildings - Witzel, Stefan; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2014)
Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.
Basic Definitions and Properties -- Finiteness Properties of G(Fq[t]) -- Finiteness Properties of G(Fq[t; t-1]) -- Affine Kac-Moody Groups -- Adding Places.
Keywords: Mathematics; Group theory; Geometry; Algebraic topology; Manifolds (Mathematics).; Complex manifolds; Mathematics; Group Theory and Generalizations; Geometry; Manifolds and Cell Complexes (incl. Diff.Topology).; Algebraic Topology; Electronic books