A motivic Fundamental Lemma
Algebraic Geometry
2026-02-12 v4 Logic
Number Theory
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 -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.
Cite
@article{arxiv.2308.12195,
title = {A motivic Fundamental Lemma},
author = {Arthur Forey and François Loeser and Dimitri Wyss},
journal= {arXiv preprint arXiv:2308.12195},
year = {2026}
}
Comments
58 pages