Winfried Frisch
The cohomology of $S$-arithmetic spin groups and related Bruhat-Tits-buildings\\ Part II: cohomological theory
Preprint series: Mathematica Gottingensis
20G25 Linear algebraic groups over local fields and their integers
20E42 Groups with a $BN$-pair; buildings, See also {51E24}
Abstract: This is the second part of my thesis, which is concerned with the cohomology
of $S$-arithmetic spin groups over number fields. After an exposition of
the relevant prerequesites from group cohomology, the geometry of the
Bruhat-Tits-building is used to get a concrete formula for the
Euler-Poincar\'e characteristic of an $S$-arithmetic spin group associated
to an positive definite quadratic space. Some examples illustrate the
connection between the geometry of the Bruhat-Tits-building and the
classification of quadratic lattices over a ring of integers.
Keywords: Bruhat-Tits-building, group cohomology, classical groups, quadratic forms, $S$-arithmetic groups