Moduli spaces of principal F-bundles

Abstract

In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) F-bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected curve over a finite field, a split reductive group G, and an irreducible algebraic representation $$\overline{\omega} $$ .of $$\overline{\omega}$$ of $$(\widehat{G})^n/Z(\widehat{G}) $$ Our spaces generalize moduli spaces of F-sheaves, studied by Drinfeld and Lafforgue, which correspond to the case G = GL r and $$\overline{\omega} $$ is the tensor product of the standard representation and its dual. The importance of the moduli spaces of F-bundles is due to the belief that Langlands correspondence is realized in their cohomology.