Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de Jacquet et Ye

Abstract

We give a geometric interpretation of the base change homomorphism between the Hecke algebra of GL(n) for an unramified extension of local fields of positive characteristic. For this, we use some results of Ginzburg, Mirkovic and Vilonen related to the geometric Satake isomorphism. We give new proof for these results in the positive characteristic case. By using that geometric interpretation of the base change homomorphism, we prove the fundamental lemma of Jacquet and Ye for arbitrary Hecke function in the the equal characteristic case.