On abelian surfaces with potential quaternionic multiplication

Details On abelian surfaces with potential quaternionic multiplication On abelian surfaces with potential quaternionic multiplication

2004-09-20

arxiv.org/abs/math/0409357v1

Mathematics

Number Theory

To appear in Bull. Belgian Math. Soc

Scientific paper

An abelian surface A over a field K has potential quaternionic multiplication if the ring End_\bar K (A) of geometric endomorphisms of A is an order in an indefinite rational division quaternion algebra. In this brief note, we study the possible structures of the ring of endomorphisms of these surfaces and we provide explicit examples of Jacobians of curves of genus two which show that our result is sharp.

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