BGG Decomposition for de Rham Sheaves on the Modular Elliptic Curve

In this thesis we present a joint work with F. Andreatta and A. Iovita about a BGG decomposition of the de Rham sheaves W_\kappa defined over the modular elliptic curves. In Chapter 1 we study the infinitesimal site of smooth rigid analytic varieties and we define the linearization and delinearization functors. In Chapter 2 we introduce the BGG decomposition for some infinite dimensional g−modules, where g is a semisimple Lie algebra. Thanks to this decomposition we compute the de Rham cohomology of the sheaves W_\kappa. The techniques presented could be used in order to study infinite dimensional g−modules over more general Shimura varieties.