The arithmetic of QM-abelian surfaces through their Galois representations

Details The arithmetic of QM-abelian surfaces through their Galois representations The arithmetic of QM-abelian surfaces through their Galois representations

2003-03-13

arxiv.org/abs/math/0303162v2

Mathematics

Number Theory

To appear in J. Algebra

Scientific paper

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.

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