Coefficient systems on the Bruhat-Tits building and pro-p Iwahori-Hecke modules
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Bibliographic Information
Coefficient systems on the Bruhat-Tits building and pro-p Iwahori-Hecke modules
（Memoirs of the American Mathematical Society, no. 1374）
American Mathematical Society, c2022
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"September 2022, volume 279, number 1374 (third of 6 numbers)"
Includes bibliographical references (p. 67-69)
Description and Table of Contents
Description
Let G be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic p.LetI be a pro-p Iwahori subgroup of G and let R be a commutative quasi-Frobenius ring. If H = R[I\G/I] 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.IfR 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.
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