Arithmetic fundamental lemma for the spherical Hecke algebra
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2024
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| Online Access: | https://hdl.handle.net/1721.1/155304 |
| _version_ | 1811097735421493248 |
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| author | Li, Chao Rapoport, Michael Zhang, Wei |
| author_facet | Li, Chao Rapoport, Michael Zhang, Wei |
| author_sort | Li, Chao |
| collection | MIT |
| description | 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). |
| first_indexed | 2024-09-23T17:04:06Z |
| format | Article |
| id | mit-1721.1/155304 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:04:06Z |
| publishDate | 2024 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1553042024-09-09T04:12:10Z Arithmetic fundamental lemma for the spherical Hecke algebra Li, Chao Rapoport, Michael Zhang, Wei 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). 2024-06-25T20:39:08Z 2024-06-25T20:39:08Z 2024-06-20 2024-06-23T03:16:35Z Article http://purl.org/eprint/type/JournalArticle 0025-2611 1432-1785 https://hdl.handle.net/1721.1/155304 Li, C., Rapoport, M. & Zhang, W. Arithmetic fundamental lemma for the spherical Hecke algebra. manuscripta math. (2024). PUBLISHER_CC en 10.1007/s00229-024-01572-0 manuscripta mathematica Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Science and Business Media LLC Springer Berlin Heidelberg |
| spellingShingle | Li, Chao Rapoport, Michael Zhang, Wei Arithmetic fundamental lemma for the spherical Hecke algebra |
| title | Arithmetic fundamental lemma for the spherical Hecke algebra |
| title_full | Arithmetic fundamental lemma for the spherical Hecke algebra |
| title_fullStr | Arithmetic fundamental lemma for the spherical Hecke algebra |
| title_full_unstemmed | Arithmetic fundamental lemma for the spherical Hecke algebra |
| title_short | Arithmetic fundamental lemma for the spherical Hecke algebra |
| title_sort | arithmetic fundamental lemma for the spherical hecke algebra |
| url | https://hdl.handle.net/1721.1/155304 |
| work_keys_str_mv | AT lichao arithmeticfundamentallemmaforthesphericalheckealgebra AT rapoportmichael arithmeticfundamentallemmaforthesphericalheckealgebra AT zhangwei arithmeticfundamentallemmaforthesphericalheckealgebra |