A Chabauty-Coleman estimate for surfaces in abelian threefolds

Abstract: Coleman's explicit version of Chabauty's theorem gives a remarkable upper bound for the number of rational points in hyperbolic curves over number fields, under a certain rank condition. This result is obtained by p-adic methods. Despite considerable efforts in this topic, higher dimensional extensions of such a bound have remained elusive. In this talk I will sketch the proof for hyperbolic surfaces contained in abelian threefolds, which provides the first case beyond the scope of curves. This is joint work with Jerson Caro.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar