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On the explicit Torsion Anomalous Conjecture

Checcoli, Sara and Veneziano, Francesco and Viada, Evelina. (2017) On the explicit Torsion Anomalous Conjecture. Transactions of the American Mathematical Society, 369. 6465 -6491.

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Official URL: http://edoc.unibas.ch/53820/

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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 produc of elliptic curves. Our main result provides a totally explicit  bound for the N'eron-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 N'eron-Tate height of the rational points of an explicit family of curves of increasing genus.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Veneziano, Francesco
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Mathematical Society
ISSN:0002-9947
e-ISSN:1088-6850
Note:Publication type according to Uni Basel Research Database: Journal article -- First published in Transactions of the American Mathematical Society in [volume and number, or year], published by the American Mathematical Society
Language:English
Identification Number:
Last Modified:21 Jun 2018 14:56
Deposited On:03 Feb 2017 13:27

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