As a sequel to our proof of the analog of Serre's conjecture for function fields in Part I of this work, we study in this paper the deformation rings of @math -dimensional mod @math representations @math of the arithmetic fundamental group @math where @math is a geometrically irreducible, smooth curve over a finite field @math of characteristic @math ( @math ). We are able to show in many cases that the resulting rings are finite flat over @math . The proof principally uses a lifting result of the authors in Part I of this two-part work, Taylor-Wiles systems and the result of Lafforgue. This implies a conjecture of A.J. de Jong for representations with coefficients in power series rings over finite fields of characteristic @math , that have this mod @math representation as their reduction.
On demontre la correspondance de Langlands pour GL r sur les corps de fonctions. La preuve generalise celle de Drinfeld en rang 2 : elle consiste a realiser la correspondance en rang r dans la cohomologie l-adique des varietes modulaires de chtoucas de Drinfeld de rang r.