On the derived category of the Iwahori-Hecke algebra
Algebraic Geometry
2021-06-29 v2 Number Theory
Representation Theory
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 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 Emerton-Helm.
Keywords
Cite
@article{arxiv.2006.03013,
title = {On the derived category of the Iwahori-Hecke algebra},
author = {Eugen Hellmann},
journal= {arXiv preprint arXiv:2006.03013},
year = {2021}
}