Generalized Greatest Common Divisors, Divisibility Sequences, and Vojta's Conjecture for Blowups

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We apply Vojta's conjecture to blowups and deduce a number of deep statements regarding (generalized) greatest common divisors on varieties, in particular on projective space and on abelian varieties. Special cases of these statements generalize earlier results and conjectures. We also discuss the relationship between generalized greatest common divisors and the divisibility sequences attached to algebraic groups, and we apply Vojta's conjecture to obtain a strong bound on the divisibility sequences attached to abelian varieties of dimension at least two.
20 pages; minor corrections (thanks to D. Abramovich, P. Corvaja, U. Zannier)

Keywords

Number Theory, Algebraic Geometry, 11G35 (Primary); 11D75, 11J25, 14G25, 14J20 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/133114

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407415
 http://arxiv.org/abs/math/0407415
 Monatsh. Math. 145 (2005), no. 4, 333--350. (MR2162351)

Collections

arXiv