Michele Pernice: Arithmetic Geometry Learning Seminar: Diophantine problems and p-adic period mappings (after Lawrence—Venkatesh)

Abstract:

In the previous lectures, we saw in details Lawrence-Venkatesh proof of the Mordell conjecture, assuming the existence of a sufficiently nice "abelian-by-finite" family. In this lecture, we will explain how to construct this family using Hurwitz spaces and Jacobians of curves. We will follow the proof given by the Authors, and, if time allows it, also sketch a more "stacky" construction of these (very specific) Hurwitz spaces.