Cohomology of buildings and finiteness properties of ̃𝐴_{𝑛}-groups

Autor:	Jacqueline Ramagge, Wayne W. Wheeler
Rok vydání:	2001
Předmět:	Algebra Sheaf cohomology Pure mathematics Alexander–Spanier cohomology Group (mathematics) Applied Mathematics General Mathematics Group cohomology Duality (mathematics) Equivariant cohomology Serre duality Cohomology Mathematics
Zdroj:	Transactions of the American Mathematical Society. 354:47-61
ISSN:	1088-6850 0002-9947
DOI:	10.1090/s0002-9947-01-02818-5
Popis:	Borel and Serre calculated the cohomology of the building associated to a reductive group and used the result to deduce that torsion-free S 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 modified to calculate the cohomology of any locally finite affine building. As an application we show that any finitely presented A ~ n \widetilde {A}_n -group is a virtual duality group. A number of other finiteness conditions for A ~ n \widetilde {A}_n -groups are also established.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::115b20eb8fe591e22b68ab0b6743a239 https://doi.org/10.1090/s0002-9947-01-02818-5 Zobrazit plný text záznamu