Winfried Frisch
The cohomology of $S$-arithmetic spin groups and related Bruhat-Tits-buildings\\ Part I: The Bruhat-Tits-building
Preprint series: Mathematica Gottingensis
20E42 Groups with a $BN$-pair; buildings, See also {51E24}
20E42 Groups with a $BN$-pair; buildings, See also {51E24}
Abstract: In this paper, which appears as number 6-8 of this preprent series,
the Bruhat-Tits-building of the spin group of a quadratic space
over a local number field is introduced and used, to compute the
cohomology of the spin goup of an unimodular lattice of dimension 8
over the ring $\mathbb{Z}[\frac{1}{2}]$ with coefficients in
$\mathbb{Z}[\frac{1}{6}]$. In the first part, the Bruhat-Tits-building
is constructed for quadratic spaces over local fields using
a description by lattices. This description includes the case of
dyadic local fields.
Keywords: Bruhat-Tits-buildings, classical groups, $S$-arithmetic groups, group cohomology