Effective computation of Darmon points

Xavier Guitart: Effective computation of Darmon points

Let $E$ be an elliptic curve over a totally real number field $F$, and let $K$ a quadratic extension of $F$. If the field $K$ is CM the classical Heegner point construction provides a method for manufacturing points on $E$ which are rational over abelian extensions of $K$. The so-called Darmon points (also known as Stark—Heegner points) are a plethora of conjectural constructions that resemble Heegner points, but for fields $K$ which are not CM. In this talk I will review some instances of Darmon points, and I will explain some joint work with Marc Masdeu on algorithms for their effective computation.