Characterizing algebraic curves with infinitely many integral points

Yuri Bilu (1) , Alvanos Paraskevas (2) , Poulakis Dimitrios (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Department of Mathematics

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.

Mots clés: algebraic curves; integral points; Siegel's theorem

Domaines: Théorie des nombres [math.NT]

Yuri Bilu, Alvanos Paraskevas, Poulakis Dimitrios. Characterizing algebraic curves with infinitely many integral points. Journal of Number Theory, 2009, 5, pp.585-590. ⟨hal-00403683⟩