On the derived category of the Iwahori–Hecke algebra
Eugen Hellmann
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.
Topics & Concepts
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