Surface abéliennes à multiplication quaternionique munie d’une structure de niveau Γ0(N)
A theorem of Mazur gives the set of possible prime degrees for rational isogenies between elliptic curves. In this paper, we are working on a similar problem in the case of abelian surfaces of type over (with ) with quaternionic multiplication (over ) endowed with a level structure. We prove the following result: for a fixed indefinite quaternion algebra of discriminant and a fixed quadratic imaginary field , there exists an effective bound such that for a prime number , not dividing the conductor of the order , there do not exist abelian surfaces such that is a maximal order of and is endowed with a level structure.
Autores: Gillibert, F.
Journal: International Journal of Number Theory
Journal Page: 1-17
Tipo de publicación: ISI
Fecha de publicación: 2016
Topics: Abelian surfaces, Galois representations, quaternionic multiplications, Shimura curves
URL de la publicación: http://www.worldscientific.com/doi/pdf/10.1142/S1793042117500725?src=recsys