Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 4, 2022 - 10:00 to 10:50

Location:

Zoom

Guest Speaker:

Institution:

ICERM

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.

Host: