Finiteness Properties of Arithmetic Groups Acting on Twin Buildings
Witzel, Stefan.
Finiteness Properties of Arithmetic Groups Acting on Twin Buildings [electronic resource] / by Stefan Witzel. - XVI, 113 p. 11 illus. online resource. - Lecture Notes in Mathematics, 2109 0075-8434 ; . - Lecture Notes in Mathematics, 2109 .
Basic Definitions and Properties -- Finiteness Properties of G(Fq[t]) -- Finiteness Properties of G(Fq[t; t-1]) -- Affine Kac-Moody Groups -- Adding Places.
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.
9783319064772
10.1007/978-3-319-06477-2 doi
Group theory.
Geometry.
Cell aggregation--Mathematics.
Algebraic topology.
Group Theory and Generalizations.
Geometry.
Manifolds and Cell Complexes (incl. Diff.Topology).
Algebraic Topology.
QA174-183
512.2
Finiteness Properties of Arithmetic Groups Acting on Twin Buildings [electronic resource] / by Stefan Witzel. - XVI, 113 p. 11 illus. online resource. - Lecture Notes in Mathematics, 2109 0075-8434 ; . - Lecture Notes in Mathematics, 2109 .
Basic Definitions and Properties -- Finiteness Properties of G(Fq[t]) -- Finiteness Properties of G(Fq[t; t-1]) -- Affine Kac-Moody Groups -- Adding Places.
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.
9783319064772
10.1007/978-3-319-06477-2 doi
Group theory.
Geometry.
Cell aggregation--Mathematics.
Algebraic topology.
Group Theory and Generalizations.
Geometry.
Manifolds and Cell Complexes (incl. Diff.Topology).
Algebraic Topology.
QA174-183
512.2