A result on the equation $x^p + y^p = z^r$ using Frey abelian varieties
  We prove a diophantine result on generalized Fermat equations of the form $x^p + y^p = z^r$ which for the first time requires the use of Frey abelian varieties of dimension $\geq 2$ in Darmon's program. For that, we provide an irreducibility criterion for the mod $\mathfrak{p}$ representations attached to certain abelian varieties of $\text{GL}_2$-type over totally real fields. 
Nicolas Billerey, Imin Chen, Luis Dieulefait and Nuno Freitas
math.NT