Towards a unified theory of canonical heights on abelian varieties

Abstract: $p$-adic heights have been a rich source of explicit functions vanishing on rational points on a curve. In this talk, we will outline a new construction of canonical $p$-adic heights on abelian varieties from $p$-adic adelic metrics, using $p$-adic Arakelov theory developed by Besser. This construction closely mirrors Zhang's construction of canonical real valued heights from real-valued adelic metrics. We will use this new construction to give direct explanations (avoiding $p$-adic Hodge theory) of the key properties of height pairings needed for the quadratic Chabauty method for rational points. This is joint work with Amnon Besser and Steffen Mueller.

number theory

Audience: researchers in the topic

Harvard number theory seminar