Outline of the argument for Mordell's conjecture

Abstract: I will present an outline of the argument for the proof of Mordell's conjecture, following Section 5 of Lawrence-Venkatesh. Specifically, I will give an overview of two key inputs: the existence of a good abelian-by-finite family (the Kodaira-Parshin family) and the finiteness of rational points whose fiber along the finite map has large Galois orbits (proven using p-adic Hodge theory). Then, I will explain how to reduce Mordell's conjecture to these key inputs.

Reference:

$\bullet$ Lawrence and Venkatesh, Diophantine problems and $p$-adic period mappings, Section 5.

algebraic geometrynumber theory

Audience: advanced learners

( slides )

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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.

Fall 2025 topic: Weil conjectures.

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.

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