%0 Journal Article
%T Uniformity of stably integral points on principally polarized abelian surfaces
%A Dan Abramovich
%A Kenji Matsuki
%J Mathematics
%D 1998
%I arXiv
%X We prove, assuming that the conjecture of Lang and Vojta holds true, that there is a uniform bound on the number of stably integral points in the complement of the theta divisor on a principally polarized abelian surface defined over a number field. This gives a uniform version, in the spirit of a result of Caporaso-Harris-Mazur, of an unconditional theorem of Faltings. We utilize recent results of Alexeev and Nakamura on complete moduli for quasi-abelian varieties. We expect that a thorough understanding of current work of Alexeev should give a more general result for abelian varieties of an arbitrary dimension with a polarizing divisor of an arbitrary degree - a proposed approach for such a generalization is given at the end of the paper.
%U http://arxiv.org/abs/math/9809023v1