Bao Châu Ngô

Nearby Cycles for Local Models of Some Shimura Varieties

Kottwitz conjectured a formula for the (semi-simple) trace of Frobenius on the nearby cycles for the local model of a Shimura variety with Iwahori-type level structure. In this paper, we prove his conjecture in the linear and symplectic cases by adapting an argument of Gaitsgory, who proved an analogous theorem in the equal characteristic case.

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 a new proof of 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 equal characteristic case.

Erratum to: "On the formal arc space of a reductive monoid"

abstract:We correct the calculation of IC functions on arc spaces of reductive monoids in [Bouthier, Ng\^o, and Sakellaridis, {\it Amer. J. Math.} {\bf 138} (2016), 81--108] which did not account for a Tate twist, corresponding to a shift in the pertinent

Le lemme fondamental pour les algèbres de Lie

L

Fibration de Hitchin et endoscopie

-function.