Ludvig Olsson: Arithmetic Geometry Learning Seminar: Diophantine problems and p-adic period mappings (after Lawrence–Venkatesh)

Abstract:

I will explain the necessary background in p-adic hodge theory needed for the Lawrence–Venkatesh paper, with a focus on crystalline representations. In particular, we will reduce the statement that the map from points in a family to Galois representations is finite to one to an algebraic statement about period maps.