Uniformity of stably integral points on principally polarized abelian surfaces
| dc.creator | Abramovich, Dan | |
| dc.creator | Matsuki, Kenji | |
| dc.date | 1998-09-05 | |
| dc.date.accessioned | 2026-07-07T05:25:53Z | |
| dc.date.available | 2026-07-07T05:25:53Z | |
| dc.description | 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. | |
| dc.description | Latex 2e, 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/9809023 | |
| dc.identifier | http://arxiv.org/abs/math/9809023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77355 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G05, 14K10, 11G10 | |
| dc.title | Uniformity of stably integral points on principally polarized abelian surfaces | |
| dc.type | text |