Bertini and Northcott
Number Theory
2021-01-05 v2
Abstract
We prove a new Bertini-type Theorem with explicit control of the genus, degree, height, and the field of definition of the constructed curve. As a consequence we provide a general strategy to reduce certain height and rank estimates on abelian varieties over a number field to the case of jacobian varieties defined over a suitable extension of .
Cite
@article{arxiv.2006.13604,
title = {Bertini and Northcott},
author = {Fabien Pazuki and Martin Widmer},
journal= {arXiv preprint arXiv:2006.13604},
year = {2021}
}
Comments
Revised and corrected version. To appear in Res. Number Theory