Arithmetic Fundamental Lemma for the spherical Hecke algebra

Fuente: arXiv
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Auteurs principaux: Li, Chao, Rapoport, Michael, Zhang, Wei
Format: Preprint
Publié: 2023
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author Li, Chao
Rapoport, Michael
Zhang, Wei
author_facet Li, Chao
Rapoport, Michael
Zhang, Wei
contents 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 $U(1)\times U(2)$.
format Preprint
id arxiv_https___arxiv_org_abs_2305_14465
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Arithmetic Fundamental Lemma for the spherical Hecke algebra
Li, Chao
Rapoport, Michael
Zhang, Wei
Number Theory
Algebraic Geometry
Representation Theory
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 $U(1)\times U(2)$.
title Arithmetic Fundamental Lemma for the spherical Hecke algebra
topic Number Theory
Algebraic Geometry
Representation Theory
url https://arxiv.org/abs/2305.14465