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arXiv · 2102.07906

Automorphic functions as the trace of Frobenius

D. Arinkin·D. Gaitsgory·D. Kazhdan·S. Raskin·N. Rozenblyum·Y. Varshavsky
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Abstract

We prove that the trace of the Frobenius endofunctor of the category of automorphic sheaves with nilpotent singular support maps isomorphically to the space of unramified automorphic functions, settling a conjecture from [AGKRRV1]. More generally, we show that traces of Frobenius-Hecke functors produce shtuka cohomologies.

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D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin, N. Rozenblyum, Y. Varshavsky. 2021-02-16. Automorphic functions as the trace of Frobenius. https://arxiv.org/abs/2102.07906

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