Studying points on varieties via varying families

Abstract: We show how Lawrence-Venkatesh's method for studying points on a variety X can be applied to curves in families. In the process, we also outline the original method. The idea is that if there exists a family over X which varys "a lot", then this strongly constrains the existence of points. This is an example of how topology influences arithmetic!

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.