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

Abstract:

In this talk I will prove Falting's theorem, given some properties of the Kodaira–Parshin Familiy and a couple of other results, the proof of which will be given in upcoming lectures. We introduce the notion of an abelian-by-finite family and show how these can be used to bound the K-rational points in an analytic disc.