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A note on divisible points of curves


Authors: M. Bays and P. Habegger
Journal: Trans. Amer. Math. Soc. 367 (2015), 1313-1328
MSC (2010): Primary 14H25; Secondary 03C64, 11G50, 11J86, 11U09
DOI: https://doi.org/10.1090/S0002-9947-2014-06494-5
Published electronically: September 4, 2014
MathSciNet review: 3280045
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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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Additional Information

M. Bays
Affiliation: Department of Mathematics and Statistics, McMaster University, Ontario, Canada
Email: mbays@sdf.org

P. Habegger
Affiliation: Fachbereich Mathematik, TU Darmstadt, Schlossgartenstrasse 7, Darmstadt, 64289 Germany
Email: habegger@mathematik.tu-darmstadt.de

DOI: https://doi.org/10.1090/S0002-9947-2014-06494-5
Received by editor(s): May 8, 2013
Published electronically: September 4, 2014
Additional Notes: The first author was partially supported by the Agence Nationale de Recherche [MODIG, Project ANR-09-BLAN-0047]
Article copyright: © Copyright 2014 American Mathematical Society