Seminar in Algebraic Geometry and Number Theory

Abstract: I will describe a method to study the locally analytic vectors in completed cohomology. I will start by the motivation and introducing the objects and then try to explain how we can introduce ideas from the hypothetical categorical Langlands correspondance to study sheaves on deformation rings to deduce Informations on completed cohomology. Along the way I will try to describe some unexpected behavior concerning p-adic modular forms, in the case of GL_3. This is a joint work with Eugen Hellmann and Benjamin Schraen.