Automorphic functions as the trace of Frobenius
D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin, N. Rozenblyum, Y., Varshavsky
TL;DR
This paper establishes a fundamental link between the trace of Frobenius endofunctors on automorphic sheaves and unramified automorphic functions, confirming a key conjecture and connecting to shtuka cohomologies.
Contribution
It proves the isomorphism between Frobenius traces on automorphic sheaves and automorphic functions, advancing the understanding of geometric Langlands correspondence.
Findings
Trace of Frobenius endofunctor maps to unramified automorphic functions
Frobenius-Hecke functors produce shtuka cohomologies
Settles a conjecture from [AGKRRV1]
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory