Towards a Unified Theory of Canonical Heights on Abelian Varieties
Towards a Unified Theory of Canonical Heights on Abelian Varieties

Padmavathi Srinivasan, Boston University
IAS  Simonyi Hall Seminar Room SH101
padic 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 padic heights on abelian varieties from padic adelic metrics, using padic Arakelov theory developed by Besser. This construction closely mirrors Zhang's construction of canonical real valued heights from realvalued adelic metrics. We will use this new construction to give direct explanations (avoiding padic Hodge theory) of the key properties of padic height pairings needed for the quadratic Chabauty method for rational points.
This is joint work with Amnon Besser and Steffen Mueller.