Uniformity of stably integral points on principally polarized abelian surfaces
Abstract
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 CaporasoHarrisMazur, of an unconditional theorem of Faltings. We utilize recent results of Alexeev and Nakamura on complete moduli for quasiabelian 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.math/9809023
 arXiv:
 arXiv:math/9809023
 Bibcode:
 1998math......9023A
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14G05;
 14K10;
 11G10
 EPrint:
 Latex 2e, 21 pages