A result on the equation $x^p + y^p = z^r$ using Frey abelian varieties
Number Theory
2016-05-10 v1
Abstract
We prove a diophantine result on generalized Fermat equations of the form which for the first time requires the use of Frey abelian varieties of dimension in Darmon's program. For that, we provide an irreducibility criterion for the mod representations attached to certain abelian varieties of -type over totally real fields.
Keywords
Cite
@article{arxiv.1605.02198,
title = {A result on the equation $x^p + y^p = z^r$ using Frey abelian varieties},
author = {Nicolas Billerey and Imin Chen and Luis Dieulefait and Nuno Freitas},
journal= {arXiv preprint arXiv:1605.02198},
year = {2016}
}