Session S21 - Galois representations and automorphic forms

No date set.

Using $\mathbb{Q}$-curves and Hecke characters to solve Fermat-type equations

Lucas Villagra Torcomian

Universidad Nacional de Córdoba, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this poster we wil see how can we adapt the classical modular method using $\mathbb{Q}$-curves and Hecke characters in order to solve the diophantine equations $x^4+dy^2=z^p$ and $x^2+dy^6=z^p$. The results obtained are in [1] and [2].

[1] Ariel Pacetti and Lucas Villagra Torcomian. $\mathbb{Q}$-curves, hecke characters and some diophantine equations, 2020.

[2] Ariel Pacetti and Lucas Villagra Torcomian. $\mathbb{Q}$-curves, hecke characters and some diophantine equations II, 2021.

Joint work with Ariel Pacetti (Center for Research and Development in Mathematics and Applications).

View abstract PDF