1.

Record Nr.

UNINA9910915706803321

Autore

Kohlhaase Jan

Titolo

Coefficient Systems on the Bruhat-Tits Building and Pro-

Pubbl/distr/stampa

Providence : , : American Mathematical Society, , 2022

©2022

ISBN

9781470472283

9781470453763

Edizione

[1st ed.]

Descrizione fisica

1 online resource (82 pages)

Collana

Memoirs of the American Mathematical Society ; ; v.279

Classificazione

20C0822E50

Disciplina

512/.2

512.2

Soggetti

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

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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"--