Finiteness Properties of Arithmetic Groups Acting on Twin Buildings

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Finiteness Properties of Arithmetic Groups Acting on Twin Buildings by Stefan Witzel, Springer International Publishing
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Author: Stefan Witzel ISBN: 9783319064772
Publisher: Springer International Publishing Publication: July 16, 2014
Imprint: Springer Language: English
Author: Stefan Witzel
ISBN: 9783319064772
Publisher: Springer International Publishing
Publication: July 16, 2014
Imprint: Springer
Language: English

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.

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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.

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