4 papers
On the conductor of a family of Frey hyperelliptic curves
Pedro-José Cazorla GarcÃa, Lucas Villagra Torcomian
In his breakthrough article, Darmon presented a program to study Generalized Fermat Equations (GFE) via abelian varieties of -type over totally real fields. So far, on…
On the generalized Fermat equation of signature
Ariel Pacetti, Lucas Villagra Torcomian
In this article we study solutions to the generalized Fermat equation using hypergeometric motives within the framework of the modular method. In doing so, we give…
A note on conductors of Frey representations at
Imin Chen, Lucas Villagra Torcomian
In 2000, Darmon introduced the notion of Frey representations within the framework of the modular method for studying the generalized Fermat equation. A central step in this progra…
On endomorphism algebras of -type abelian varieties and Diophantine applications
Franco Golfieri Madriaga, Ariel Pacetti, Lucas Villagra Torcomian
Let and be two different newforms without complex multiplication having the same coefficient field. The main result of the present article proves that a congruence between…