On the derived category of the Iwahori–Hecke algebra-Reference-Cited by-同舟云学术

On the derived category of the Iwahori–Hecke algebra

Published:2023-05 Issue:5 Volume:159 Page:1042-1110
ISSN:0010-437X
Container-title:Compositio Mathematica
language:en
Short-container-title:Compositio Math.

Author:

Hellmann Eugen

Abstract

We state a conjecture that relates the derived category of smooth representations of a

$p$

-adic split reductive group with the derived category of (quasi-)coherent sheaves on a stack of L-parameters. We investigate the conjecture in the case of the principal block of

${\rm GL}_n$

by showing that the functor should be given by the derived tensor product with the family of representations interpolating the modified Langlands correspondence over the stack of L-parameters that is suggested by the work of Helm and of Emerton and Helm.

Publisher

Wiley

Subject

Algebra and Number Theory

Reference34 articles.

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3. Proof of the Deligne-Langlands conjecture for Hecke algebras

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