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Title:
Towards a Unified Theory of Canonical Heights on Abelian Varieties
Speaker:
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 p-adic height pairings needed for the quadratic Chabauty method for rational points. This is joint work with Amnon Besser and Steffen Mueller.
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