Sur le lemme fondamental pour les groupes unitaires

2002/12/18 by Gérard Laumon, Gerard Laumon, Laumon, Gerard
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0212245

plain tex, 26 pages, in French

arxiv created 2002/12/18 · arxiv updated 2009/11/30

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.

Related

• Purity of the anisotropic affine Springer fibers for GL_n
• On the fundamental domain of affine Springer fibers
• A decomposition theorem for the affine Springer fibers
• On the dependence of the affine Springer fibers on their root valuation datum
• On the geometric fundamental lemma of Kottwitz