Coefficient Systems on the Bruhat-Tits Building and Pro-

• Autore: Kohlhaase Jan
• Pubblicazione: Providence : , : American Mathematical Society, , 2022; ©2022
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (82 pages)
• Disciplina: 512/.2; 512.2
• Soggetto topico: Buildings (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
• Classificazione: 20C0822E50
• Nota di contenuto: 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.
• Sommario/riassunto: "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"--
• Titolo autorizzato: Coefficient Systems on the Bruhat-Tits Building and Pro-
• ISBN: 9781470472283; 9781470453763
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910915706803321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society