On the explicit Torsion Anomalous Conjecture
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- by S. Checcoli, F. Veneziano and E. Viada PDF
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Abstract:
The Torsion Anomalous Conjecture states that an irreducible variety $V$ embedded in a semi-abelian variety contains only finitely many maximal $V$-torsion anomalous varieties. In this paper we consider an irreducible variety embedded in a product of elliptic curves. Our main result provides a totally explicit bound for the Néron-Tate height of all maximal $V$-torsion anomalous points of relative codimension one in the non-CM case, and an analogous effective result in the CM case. As an application, we obtain the finiteness of such points. In addition, we deduce some new explicit results in the context of the effective Mordell-Lang Conjecture; in particular we bound the Néron-Tate height of the rational points of an explicit family of curves of increasing genus.References
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Additional Information
- S. Checcoli
- Affiliation: Institut Fourier, 100 rue des Maths, BP74 38402 Saint-Martin-d’Hères Cedex, France
- MR Author ID: 924817
- Email: sara.checcoli@univ-grenoble-alpes.fr
- F. Veneziano
- Affiliation: Mathematisches Institut, Universität Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland
- MR Author ID: 966417
- ORCID: 0000-0002-2225-7769
- Email: francesco.veneziano@unibas.ch
- E. Viada
- Affiliation: Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3-5, D-37073 Göttingen, Germany
- Address at time of publication: ETH Zurich, Rämistrasse 101, 8092 Zurich, Switzerland
- Email: evelina.viada@math.ethz.ch
- Received by editor(s): July 2, 2013
- Received by editor(s) in revised form: September 29, 2015
- Published electronically: March 6, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 6465-6491
- MSC (2010): Primary 11G50; Secondary 14G40
- DOI: https://doi.org/10.1090/tran/6893
- MathSciNet review: 3660229