A motivic Fundamental Lemma
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912895281922048 |
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| author | Forey, Arthur Loeser, François Wyss, Dimitri |
| author_facet | Forey, Arthur Loeser, François Wyss, Dimitri |
| contents | In this paper we prove motivic versions of the Langlands-Shelstad Fundamental Lemma and Ngô's Geometric Stabilization. To achieve this, we follow the strategy from the recent proof by Groechenig, Wyss and Ziegler which avoided the use of perverse sheaves using instead $p$-adic integration and Tate duality. We make a key use of a construction of Denef and Loeser which assigns a virtual motive to any definable set in the theory of pseudo-finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12195 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A motivic Fundamental Lemma Forey, Arthur Loeser, François Wyss, Dimitri Algebraic Geometry Logic Number Theory 03C65 14E18 11S37 14D24 14H60 In this paper we prove motivic versions of the Langlands-Shelstad Fundamental Lemma and Ngô's Geometric Stabilization. To achieve this, we follow the strategy from the recent proof by Groechenig, Wyss and Ziegler which avoided the use of perverse sheaves using instead $p$-adic integration and Tate duality. We make a key use of a construction of Denef and Loeser which assigns a virtual motive to any definable set in the theory of pseudo-finite fields. |
| title | A motivic Fundamental Lemma |
| topic | Algebraic Geometry Logic Number Theory 03C65 14E18 11S37 14D24 14H60 |
| url | https://arxiv.org/abs/2308.12195 |