Moduli spaces of Λ-modules on abelian varieties

Abstract

We study the moduli space MX(Λ,n) of semistable Λ-modules of vanishing Chern classes over an abelian variety X, where Λ belongs to a certain subclass of D-algebras. In particular, for Λ=DX (resp. Λ=Sym•TX) we obtain a description of the moduli spaces of flat connections (resp. Higgs bundles).We give a description of MX(Λ,n) in terms of a symmetric product of a certain fibre bundle over the dual abelian variety Xˆ. We also give a moduli interpretation to the associated Hilbert scheme as the classifying space of Λ-modules with extra structure. Finally, we study the non-abelian Hodge theory associated to these new moduli spaces.