On abelian surfaces with potential quaternionic multiplication
数论
2007-05-23 v1 代数几何
摘要
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.
引用
@article{arxiv.math/0409357,
title = {On abelian surfaces with potential quaternionic multiplication},
author = {Luis Dieulefait and Victor Rotger},
journal= {arXiv preprint arXiv:math/0409357},
year = {2007}
}
备注
To appear in Bull. Belgian Math. Soc