Institut Henri Poincaré

À la redécouverte des points rationnels

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p-adic approaches to rational points on curves

Bjorn Poonen

In these four lectures, I will describe Chabauty's p-adic method for determining the rational points on a curve whose Jacobian has rank less than the genus, hint at Kim's nonabelian generalization, and finally discuss the recent paper of Lawrence and Venkatesh that uses p-adic period maps to give a new proof of Faltings\'s theorem.



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