Geodesic
Higher finiteness properties of reductive arithmetic groups in positive characteristic: The Rank Theorem
Kai-Uwe Bux1 ; Ralf Köhl2 ; Stefan Witzel3
1 Fakultä fü Mathematik, Universität Bielefeld, Universitästrasse 25, 33501 Bielefeld, Germany
2 Mathematisches Institut, Justus-Liebig-Universität Giessen, Arndstrasse 2, 35392 Giessen, Germany
3 Mathematisches Institute, Universitä t M&uumlnster, Einsteinstrasse 62, 48148 Münster, Germany
Annals of mathematics, Tome 177 (2013) no. 1, pp. 311-366.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in a noncommutative isotropic absolutely almost simple group $\mathcal{G}$ over a global function field is one less than the sum of the local ranks of $\mathcal{G}$ taken over the places in $S$. This determines the finiteness properties for $S$-arithmetic subgroups in isotropic reductive groups, confirming the conjectured finiteness properties for this class of groups.
DOI : 10.4007/annals.2013.177.1.6

Kai-Uwe Bux 1 ; Ralf Köhl 2 ; Stefan Witzel 3

1 Fakultä fü Mathematik, Universität Bielefeld, Universitästrasse 25, 33501 Bielefeld, Germany
2 Mathematisches Institut, Justus-Liebig-Universität Giessen, Arndstrasse 2, 35392 Giessen, Germany
3 Mathematisches Institute, Universitä t M&uumlnster, Einsteinstrasse 62, 48148 Münster, Germany 
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Kai-Uwe Bux; Ralf Köhl; Stefan Witzel. Higher finiteness properties of reductive arithmetic groups in positive characteristic: The Rank Theorem. Annals of mathematics, Tome 177 (2013) no. 1, pp. 311-366. doi : 10.4007/annals.2013.177.1.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.177.1.6/

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