English

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 KK to the case of jacobian varieties defined over a suitable extension of KK.

Keywords

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

R2 v1 2026-06-23T16:35:03.663Z