主极化阿贝尔曲面上稳定整点的均匀性
Uniformity of stably integral points on principally polarized abelian surfaces
摘要：
我们证明，假设朗和Vojta的猜想成立，有一个统一的界限上的稳定整点的数量在补充的θ因子上定义的一个主要极化阿贝尔表面上的数域。这给出了一个统一的版本，在精神上的一个结果Caporaso-Harris-Mazur，一个无条件定理的Faltings。我们利用Alexeev和Nakamura关于拟阿贝尔簇的完全模的最新结果。我们希望，一个彻底的了解目前的工作阿列克谢耶夫应该得到一个更普遍的结果为阿贝尔簇的任意维度的极化因子的任意程度-一个建议的方法，这样的推广给出在最后的文件。
英文摘要：
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.
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