A note on divisible points of curves

Abstract

Let C C be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3 3 . We partially answer a question posed by Levin on points on C C for which a non-trivial power lies again on C C . Our results have connections to Zilber’s Conjecture on Intersections with Tori and yield to methods arising in transcendence theory and the theory of o-minimal structures.