Families of trianguline representations, finite slope spaces and eigenvarieties

• Applicant: Professor Dr. Eugen Hellmann
• Subject Area: Mathematics
• Term: from 2012 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 221576595

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
• Host: Professor Dr. Jean-Francois Dat