**Emilio Franco**

University of Campinas, Brazil

October 1, 2015

**Moduli spaces of Lambda-modules on abelian varieties**:
Let Lambda be a D-algebra in the sense of Bernstein and Beilinson. Higgs bundles, vector bundles with flat connections, co-Higgs
bundles etc. are examples of Lambda-modules for particular choices of
Lambda. Simpson studied the moduli problem for the classification of
Lambda-modules over Kahler varieties, proving the existence of a moduli space Lambda-modules.
Using the Polishchuck-Rothstein transform for modules of D-algebras over abelian varieties, we obtain a description of the moduli spaces of Lambda-modules of rank 1. We also proof that polystable Lambda module decompose as a direct sum of rank 1 Lambda-modules. This allow us to describe the module spaces in arbitrary rank.