Magnus Carlson: Arithmetic Geometry Learning Seminar - Diophantine problems and p-adic period mappings

Abstract:
I will continue by explaining the structure of Lawrence—Venkatesh’s proof of Faltings’s theorem. We have explained how to show that there are only finitely many semi-simple global representations of the form we are after, in this talk, we will show how one can combine this with p-adic Hodge theory to show finiteness of rational points.