English

Vojta's Inequality and Rational and Integral Points of Bounded Degree on Curves

Number Theory 2007-05-23 v1

Abstract

Let C in C_1xC_2 be a curve of type (d_1,d_2) in the product of the two curves C_1 and C_2. Let d be a positive integer. We prove that if a certain inequality involving d_1, d_2, d, and the genera of the curves C_1, C_2, and C is satisfied, then the set of points P in C(\kbar) with [k(P):k]<=d is finite for any number field k. We prove a similar result for integral points of bounded degree on C. These results are obtained as consequences of an inequality of Vojta which generalizes the Roth-Wirsing theorem to curves.

Keywords

Cite

@article{arxiv.math/0601686,
  title  = {Vojta's Inequality and Rational and Integral Points of Bounded Degree on Curves},
  author = {Aaron Levin},
  journal= {arXiv preprint arXiv:math/0601686},
  year   = {2007}
}

Comments

11 pages