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Instituto de Matemáticas Aplicadas UCV

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 \mathbb{Q} (with \mathbb{Q}) 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 Volume:

Journal Issue:

Journal Page: 1-17

Tipo de publicación: ISI

Fecha de publicación: 2016

Topics: Abelian surfaces, Galois representations, quaternionic multiplications, Shimura curves

DOI: 10.1142/S1793042117500725

URL de la publicación: http://www.worldscientific.com/doi/pdf/10.1142/S1793042117500725?src=recsys

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