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arXiv · 2308.12195

A motivic Fundamental Lemma

Arthur Forey·François Loeser·Dimitri Wyss
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Abstract

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.

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Arthur Forey, François Loeser, Dimitri Wyss. 2023-08-23. A motivic Fundamental Lemma. https://doi.org/10.2140/gt.2026.30.2043

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