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arXiv · 1502.07148

G\'eom\'etrisation du lemme fondamental pour l'alg\`ebre de Hecke

Alexis Bouthier
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Abstract

This article is the third one of the series \cite{Bt1}-\cite{Bt2} on Hitchin-Frenkel-Ngo fibration and Vinberg semigroup. Ngo \cite{N} proved the fundamental lemma for Lie algebras in equal characteristics as a consequence of geometric stabilization. This article show the geometric stabilization in the group case which was conjectured by Frenkel and Ngo \cite{FN}. Along the proof, we establish an identity between orbital integrals, which is analog to Langlands-Shelstad fundamental lemma. From this equality, we deduce a formula for Langlands-Shelstad transfer factors which was previously only known for Lie algebras.

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Alexis Bouthier. 2015-02-25. G\'eom\'etrisation du lemme fondamental pour l'alg\`ebre de Hecke. https://arxiv.org/abs/1502.07148

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