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arXiv · 2006.03013

On the derived category of the Iwahori-Hecke algebra

Eugen Hellmann
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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.

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Eugen Hellmann. 2020-06-04. On the derived category of the Iwahori-Hecke algebra. https://arxiv.org/abs/2006.03013

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