Coefficient Systems on the Bruhat-Tits Building and Pro-p Iwahori-Hecke Modules.

Format:

Book

Author/Creator:

Kohlhaase, Jan.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.279

Language:

English

Subjects (All):

Buildings (Group theory).

Hecke algebras.

Physical Description:

1 online resource (82 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2022.

Summary:

"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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Kohlhaase, Jan Coefficient Systems on the Bruhat-Tits Building and Pro-p Iwahori-Hecke Modules

ISBN:

9781470472283

OCLC:

1343248781