This project lies on the crossroads between Algebraic Geometry, Algebraic Number theory and the theory of automorphic forms. I want to study families of p-adic representations of p-adic Galois groups, and, more precisely, the class of so called trianguline representations. This study should yield on the one hand a new approach to Kisins finite slope space, on the other hand it should generalize this construction. Then I want to compare the resulting spaces with eigenvarieties, i.e with spaces parametrizing p-adic families of automorphic forms. Further I will discuss the connection with the Langlands program and the Fontaine-Mazur conjecture, i.e. with the conjectural connection between Galois representations and automorphic forms.
DFG Programme
Research Fellowships
International Connection
France
