The arithmetic of QM-abelian surfaces through their Galois representations

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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 endomorphisms on these abelian varieties and the images of the Galois representations on their Tate modules. We illustrate our results with several explicit examples.
To appear in J. Algebra

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Number Theory, Algebraic Geometry, 11G18; 14G35

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http://salesiana.dossiersoluciones.com/handle/123456789/66780

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303162
 http://arxiv.org/abs/math/0303162

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arXiv