03717nam 22005533 450 991091570680332120231110223520.09781470472283(electronic bk.)9781470453763(MiAaPQ)EBC29731922(Au-PeEL)EBL29731922(CKB)24767777300041(OCoLC)1343248781(PPN)270358978(EXLCZ)992476777730004120220904d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierCoefficient Systems on the Bruhat-Tits Building and Pro-1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (82 pages)Memoirs of the American Mathematical Society ;v.279Print version: Kohlhaase, Jan Coefficient Systems on the Bruhat-Tits Building and Pro- Providence : American Mathematical Society,c2022 9781470453763 Cover -- Title page -- Introduction -- Chapter 1. A reminder on the Bruhat-Tits building -- 1.1. Stabilizers and Bruhat decompositions -- 1.2. Hecke algebras -- Chapter 2. Coefficient systems -- 2.1. Coefficient systems and diagrams -- 2.2. Acyclic coefficient systems on the standard apartment -- Chapter 3. The equivalence of categories -- 3.1. Representations and Hecke modules of stabilizer groups -- 3.2. Coefficient systems and pro- Iwahori-Hecke modules -- Chapter 4. Applications to representation theory -- 4.1. Homology in degree zero -- 4.2. Homotopy categories and their localizations -- 4.3. The functor to generalized ( ,Γ)-modules -- Bibliography -- Back Cover."Let G be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic p. Let I be a pro-p Iwahori subgroup of G and let R be a commutative quasi-Frobenius ring. If denotes the pro-p Iwahori-Hecke algebra of G over R we clarify the relation between the category of H-modules and the category of G-equivariant coefficient systems on the semisimple Bruhat-Tits building of G. If R is a field of characteristic zero this yields alternative proofs of the exactness of the Schneider-Stuhler resolution and of the Zelevinski conjecture for smooth G-representations generated by their I-invariants. In general, it gives a description of the derived category of H-modules in terms of smooth G-representations and yields a functor to generalized ()- modules extending the constructions of Colmez, Schneider and Vigneras"--Provided by publisher.Memoirs of the American Mathematical Society Buildings (Group theory)Hecke algebrasGroup theory and generalizations -- Representation theory of groups -- Hecke algebras and their representationsmscTopological groups, Lie groups -- Lie groups -- Representations of Lie and linear algebraic groups over local fieldsmscBuildings (Group theory)Hecke algebras.Group theory and generalizations -- Representation theory of groups -- Hecke algebras and their representations.Topological groups, Lie groups -- Lie groups -- Representations of Lie and linear algebraic groups over local fields.512/.2512.220C0822E50mscKohlhaase Jan1779016MiAaPQMiAaPQMiAaPQ9910915706803321Coefficient Systems on the Bruhat-Tits Building and Pro-4302267UNINA