Proof of the new gap principle 1

Abstract: Over the next two talks to prove Proposition 7.1 of [DGH] which, roughly-speaking, bounds the number of points on a curve within a fixed distance of a given point. In this talk we prepare for the proof of this proposition by proving a series of lemmas from section 6 of [DGH]. Specifically, after stating Proposition 7.1 of [DGH], we will prove Theorem 6.2 (which shows non-degeneracy of a certain subvariety of the universal abelian variety) followed by Lemmas 6.3 and 6.1 (which will be used to obtain the bound in Proposition 7.1).

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.