Arithmetic Fundamental Lemma for the spherical Hecke algebra
Number Theory
2024-05-24 v2 Algebraic Geometry
Representation Theory
Abstract
We define Hecke correspondences and Hecke operators on unitary RZ spaces and study their basic geometric properties, including a commutativity conjecture on Hecke operators. Then we formulate the Arithmetic Fundamental Lemma conjecture for the spherical Hecke algebra. We also formulate a conjecture on the abundance of spherical Hecke functions with identically vanishing first derivative of orbital integrals. We prove these conjectures for the case .
Cite
@article{arxiv.2305.14465,
title = {Arithmetic Fundamental Lemma for the spherical Hecke algebra},
author = {Chao Li and Michael Rapoport and Wei Zhang},
journal= {arXiv preprint arXiv:2305.14465},
year = {2024}
}
Comments
50 pages. Revised, incorporating suggestions of the referee. To appear in Manuscripta Math