Characterizing algebraic curves with infinitely many integral points

Abstract

A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinity. In this paper we give necessary and sufficient conditions for C to have infinitely many S-integral points.Comment: Int. J. Number Th. 5 (2009), 585-59