Coefficient systems on the Bruhat-Tits building and pro-p Iwahori-Hecke modules / Jan Kohlhaase.

Format:

Book

Author/Creator:

Kohlhaase, Jan, author.

Series:

Memoirs of the American Mathematical Society ; no.1374.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1374

Language:

English

Subjects (All):

Buildings (Group theory).

Hecke algebras.

Group algebras.

Group theory.

Homology theory.

Representations of groups.

Physical Description:

v, 69 pages : illustrations ; 26 cm

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:

A reminder on the Bruhat-Tits building

Coefficient systems

The equivalence of categories

Applications to representation theory.

Notes:

Includes bibliographical references.

ISBN:

9781470453763

1470453762

OCLC:

1343651837