Shimura-Kurven, Endomorphismen und q-Parameter

Abstract

In this thesis we study arithmetic properties of special Shimura curves. We give a p-adic local description at CM points of a Shimura curve as locus in the deformation space of the reduced Abelian variety. We give explicit equations for this locus in the considered cases. As a space this locus is a torus and the torsion points correspond to CM lifts of the Abelian variety. We also give an explicit construction of special Abelian surfaces, namely those which are of type QM and are isogenous to the product of elliptic curves.