English

Nevanlinna Theory and Rational Points

Number Theory 2009-09-25 v1

Abstract

S. Lang conjectured in 1974 that a hyperbolic algebraic variety defined over a number field has only finitely many rational points, and its analogue over function fields. We discuss the Nevanlinna-Cartan theory over function fields of arbitrary dimension and apply it for Diophantine property of hyperbolic projective hypersurfaces (homogeneous Diophantine equations) constructed by Masuda-Noguchi. We also deal with the finiteness property of SS-units points of those Diophantine equations over number fields.

Keywords

Cite

@article{arxiv.math/9604222,
  title  = {Nevanlinna Theory and Rational Points},
  author = {Junjiro Noguchi},
  journal= {arXiv preprint arXiv:math/9604222},
  year   = {2009}
}