Sur le lemme fondamental pour les groupes unitaires

TL;DR

This paper proves a geometric version of the fundamental lemma for unitary groups, assuming the purity conjecture for affine Springer fibers, and introduces a novel link to compactified Jacobians.

Contribution

It establishes a geometric analog of the fundamental lemma for unitary groups based on the purity conjecture, connecting affine Springer fibers with compactified Jacobians.

Findings

Proves the geometric fundamental lemma for unitary groups.

Links affine Springer fibers to compactified Jacobians.

Assumes the purity conjecture for affine Springer fibers.

Abstract

Assuming the purity conjecture for the affine Springer fibers which has been formulated by Goresky, Kottwitz and MacPherson, we prove a geometric analog of the fundamental lemma for unitary groups. Our approach is similar to the one of Goresky, Kottwitz and MacPherson. Our main new ingredient is the link between affine Springer fibers and compactified Jacobians which is described in math.AG/0204109.