34 citations · 42 across the 11 of their papers we have counts for
5 papers · 1 filter
Modularity of rigid Calabi-Yau threefolds over Q
Luis Dieulefait, Jayanta Manoharmayum
We prove modularity for a huge class of rigid Calabi-Yau threefolds over $\Q$. In particular we prove that every rigid Calabi-Yau threefold with good reduction at 3 and 7 is modula…
Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture
Luis Dieulefait
In a previous article, we have proved a result asserting the existence of a compatible family of Galois representations containing a given crystalline irreducible odd two-dimension…
Modularity of abelian surfaces with Quaternionic Multiplication
Luis Dieulefait
We prove that any abelian surface defined over $\Q$ of -type having quaternionic multiplication and good reduction at 3 is modular. We generalize the result to higher dimensi…
Modular congruences, Q-curves, and the diophantine equation x^4 + y^4 = z^p
Luis Dieulefait
We prove two results concerning the generalized Fermat equation . In particular we prove that the First Case is true if .
The arithmetic of QM-abelian surfaces through their Galois representations
Luis V. Dieulefait, V. Rotger
This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomo…