English

A Bogomolov type statement for function fields

Number Theory 2013-07-16 v1

Abstract

Let k be a an algebraically closed field of arbitrary characteristic, and we let h be the usual Weil height for the n-dimensional affine space corresponding to the function field k(t) (extended to its algebraic closure). We prove that for any affine variety V defined over the algebraic closure of k(t), there exists a positive real number c such that if P is an algebraic point of V and h(P)< c, then P has its coordinates in k.

Keywords

Cite

@article{arxiv.1307.3748,
  title  = {A Bogomolov type statement for function fields},
  author = {Dragos Ghioca},
  journal= {arXiv preprint arXiv:1307.3748},
  year   = {2013}
}
R2 v1 2026-06-22T00:51:08.733Z