Automorphic functions as the trace of Frobenius

Automorphic functions as the trace of Frobenius

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 prod...

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Veröffentlicht in:arXiv.org 2022-06
Hauptverfasser: Arinkin, D, Gaitsgory, D, Kazhdan, D, Raskin, S, Rozenblyum, N, Varshavsky, Y
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Sprache:eng
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Sheaves
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Zusammenfassung: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.
ISSN:2331-8422