Barcelona Fall Workshop on Number Theory

Modular forms over fields of mixed signature and algebraic points in elliptic curves


Xavier Guitart


I will describe a conjectural construction of algebraic points on certain modular elliptic curves defined over fields of mixed signature. The points are defined by means of integrals of the modular form attached to the elliptic curve in a way that resembles, and is inspired by, Darmon's construction in the totally real field case. I will also discuss some numerical computations that give evidence for the conjecture. This is joint work with Marc Masdeu and Haluk Sengun.


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