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Nevanlinna Theory and Rational Points

Junjiro Noguchi
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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 $S$-units points of those Diophantine equations over number fields.

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Junjiro Noguchi. 1996-04-10. Nevanlinna Theory and Rational Points. https://arxiv.org/abs/math/9604222

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