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Recent results on the arithmetic of Darmon points on abelian varieties

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I will explain how, building on general results on p-adic uniformizations of Jacobians of Shimura curves, one can define Darmon points on Shimura curves and modular abelian varieties and formulate precise conjectures on their rationality. These points are vast generalizations of Darmon’s Stark-Heegner points on elliptic curves. Finally, I will describe recent results on the arithmetic of Darmon points on abelian varieties, with special attention to the case of elliptic curves. This talk is based on joint work with Matteo Longo (Universit√† di Padova) and Victor Rotger (Universitat Polit√®cnica de Catalunya).

This talk is part of the Number Theory Seminar series.

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