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On the explicit Torsion Anomalous Conjecture
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
ID 3726634
Author(s) Checcoli, Sara; Veneziano, Francesco; Viada, Evelina
Author(s) at UniBasel Veneziano, Francesco ;
Year 2016
Year: comment (Accepted on 21.12.205. )
Title On the explicit Torsion Anomalous Conjecture
Journal Transactions of the American Mathematical Society
Pages / Article-Number 25
Keywords Heights, Algebraic Varieties
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 explicită
bound for the N\’eron-Tate height of all maximal $V$-torsion anomalous points of relative codimension
one, in theă non CM case, and an analogous effective result in the CM case.ă
As an application, we obtain theă 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.
Publisher Transactions of the American Mathematical Society
Full Text on edoc ;
Additional Information The paper has been accepted at the end of 2015, but I didn’t insert it as a
published paper for the 2016 report.

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