Arithmetic Fundamental Lemma for the spherical Hecke algebra
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913358749368320 |
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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 |