Lambda-modules and holomorphic Lie algebroids

The thesis is concerned with the construction and the study of moduli spaces of holomorphic Lie algebroid connections. It provides a classification of sheaves of almost polynomial filtered algebras on a smooth projective complex variety in terms of holomorphic Lie algebroids and their cohomology classes. This permits to build moduli spaces of holomorphic Lie agebroid connections via Simpson’s formalism of Lambda-modules. Furthermore, the deformation theory of such connections is studied, and the germ of their moduli spaces in the rank two case is computed when the base variety is a curve.