Arithmetic fundamental lemma for the spherical Hecke algebra
Name
229_2024_Article_1572.pdf
Size
660.85 KB
Format
Adobe PDF
Checksum (MD5)
944fd16bf712a4647eec42a2a162e7e8
Author(s)
Li, Chao
Rapoport, Michael
Zhang, Wei
Date Issued
June 20, 2024
Journal
manuscripta mathematica
Publisher
Springer Science and Business Media LLC
Citation
Li, C., Rapoport, M. & Zhang, W. Arithmetic fundamental lemma for the spherical Hecke algebra. manuscripta math. (2024).
Version
Final published version
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 U(1)×U(2).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00229-024-01572-0
