Lawrence--Venkatesh and the Section Conjecture

Abstract: Grothendieck's famous Section Conjecture predicts that the set of rational points on a smooth projective curve $X$ of genus at least two should be equal to a certain "section set" defined purely in terms of the etale fundamental group of $X$. Despite several decades of interest, this section set remains highly mysterious, and we do not even know whether the section set is finite, in accordance with the Mordell Conjecture.

In this talk I will describe work with Jakob Stix, in which we applied the method of Lawrence--Venkatesh to this question and proved a certain shadow of this expected finiteness result.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper )

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MIT number theory seminar

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