A motivic Fundamental Lemma
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Pré-publication ou Document de travail
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Title :
A motivic Fundamental Lemma
Author(s) :
Forey, Arthur [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Loeser, François [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Wyss, Dimitri [Auteur]
Département de Mathématiques - EPFL
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Loeser, François [Auteur]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Wyss, Dimitri [Auteur]
Département de Mathématiques - EPFL
Publication date :
2023-08-23
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
In this paper we prove motivic versions of the Langlands-Shelstad Fundamental Lemma and Ng\^o's Geometric Stabilization. To achieve this, we follow the strategy from the recent proof by Groechenig, Wyss and Ziegler which ...
Show more >In this paper we prove motivic versions of the Langlands-Shelstad Fundamental Lemma and Ng\^o'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.Show less >
Show more >In this paper we prove motivic versions of the Langlands-Shelstad Fundamental Lemma and Ng\^o'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.Show less >
Language :
Anglais
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53 pages
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Submission date :
2025-01-24T14:56:24Z
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