Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Cohomology Of Buildings And Finiteness Properties Of An-Groups, Jacqueline Ramagge, Wayne W. Wheeler
Cohomology Of Buildings And Finiteness Properties Of An-Groups, Jacqueline Ramagge, Wayne W. Wheeler
Faculty of Informatics - Papers (Archive)
Borel and Serre calculated the cohomology of the building associated to a reductive group and used the result to deduce that torsion-free S-arithmetic groups are duality groups. By replacing their group-theoretic arguments with proofs relying only upon the geometry of buildings, we show that Borel and Serre's approach can be modied to calculate the cohomology of any locally nite ane building. As an application we show that any nitely presented e An-group is a virtual duality group. A number of other niteness conditions for e An-groups are also established.