A note on divisible points of curves

Bays, M.; Habegger, P.

doi:10.1090/S0002-9947-2014-06494-5

A note on divisible points of curves
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by M. Bays and P. Habegger PDF

Trans. Amer. Math. Soc. 367 (2015), 1313-1328 Request permission

Abstract:

Let $C$ be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least $3$. We partially answer a question posed by Levin on points on $C$ for which a non-trivial power lies again on $C$. 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.

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