Moduli spaces of principal F-bundles

2002/05/31 by Yakov Varshavsky
Mathematics · #math.AG #math.RT #msc:14G35 #msc:14H60 #msc:11F70

paper · pdf

published as Sel. Math., New ser. 10 (2004) 131-166 · 37 pages, revised version

arxiv created 2004/08/31 · arxiv updated 2009/11/30

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 \ov\om of (\checkG)ⁿ/Z(\checkG). Our spaces generalize moduli spaces of F-sheaves, studied by Drinfeld and Lafforgue, which correspond to the case G=GL_r and \ov\om 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 should be realized in their cohomology.

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