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Integral points of bounded degree on affine curves

Part of:Entire and meromorphic functions, and related topicsArithmetic algebraic geometry

Published online by Cambridge University Press:  26 November 2015

Aaron Levin
Aaron Levin*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA email adlevin@math.msu.edu
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Abstract

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We generalize Siegel’s theorem on integral points on affine curves to integral points of bounded degree, giving a complete characterization of affine curves with infinitely many integral points of degree $d$ or less over some number field. Generalizing Picard’s theorem, we prove an analogous result characterizing complex affine curves admitting a nonconstant holomorphic map from a degree $d$ (or less) analytic cover of $\mathbb{C}$.

Keywords

integral pointsbounded degreeSiegel’s theoremPicard’s theorem

MSC classification

Primary:11G30: Curves of arbitrary genus or genus $ne 1$ over global fields
Secondary:30D35: Distribution of values, Nevanlinna theory

Information

Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 4 , April 2016, pp. 754 - 768
Copyright
© The Author 2015 

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