Integral points of bounded degree on affine curves

Abstract

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 $\mathbb{C}$.

References in corpus (1)

• On the Zariski-Density of Integral Points on a Complement of Hyperplanes in P^n

Cited by in corpus (3)

• Non-archimedean hyperbolicity and applications
• Cyclic Cubic Points on Higher Genus Curves
• Fields generated by points on superelliptic curves