Winfried Frisch
The cohomology of $S$-arithmetic spin groups and related Bruhat-Tits-buildings\\ Part III: The cohomology of Spin$(8,Z[\frac{1}{2}])$
Preprint series: Mathematica Gottingensis

MSC:

20E42 Groups with a $BN$-pair; buildings, See also {51E24}

20G25 Linear algebraic groups over local fields and their integers

Abstract: This is the third part of my thesis, which is concerned with the
cohomology of $S$-arithmetic spin groups over number fields.
The results of the first and the second part over the Bruhat-Tits-building
and its relations to the classification of quadratic forms over $\mathbb{Z}$
and to group cohomology are used to compute the cohomology of the
spin group over the ring $\mathbb{Z}[\frac{1}{2}]$, which is associated
to an even unimodular quadratic lattice of dimension 8 over $\mathbb{Z}$,
with coefficients in the ring $\mathbb{Z}[\frac{1}{6}]$ (resp. with
coefficients in the prime fields of characteristic 5 and 7).
Keywords: Bruhat-Tits-buildings, group cohomology, $S$-arithmetic groups, quadratic forms