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Séminaire de Mathématique
# p-adic height pairings and integral points on hyperelliptic curves

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Amphithéâtre Léon Motchane (I.H.E.S.)
### Amphithéâtre Léon Motchane

#### I.H.E.S.

Le Bois Marie
35, route de Chatres
91440 Bures-sur-Yvette

Description

I will discuss a method, based on p-adic height pairings, for determining the integral solutions of certain hyperelliptic equations.
The method produces, for a hyperelliptic curve over the rational numbers whose rank equals its genus, an explicit function on the p-adic points on the curve that takes finitely many explicitly determined values on the integral points. The proof goes via p-adic Arakelov theory.
Time permitting I will explain how one can use the generated function to effectively find the integral points and suggest some potential applications.

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