Third Italian Number Theory Meeting

Some explicit cases of the Torsion Anomalous Conjecture

speaker: Francesco Veneziano (Universität Basel)

abstract: The Torsion Anomalous Conjecture states that an algebraic variety V in a semi-abelian variety contains finitely many maximal torsion anomalous subvarieties. In a paper with Sara Checcoli and Evelina Viada we prove some new cases of this conjecture for V a weak-transverse variety in a product of elliptic curves. Our main result provides a totally explicit bound for the Neron-Tate height of all 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 new explicit results in the context of the effective Mordell-Lang Conjecture; in particular we bound the Neron-Tate height of the rational points of an explicit family of curves of increasing genus.

timetable:
Mon 21 Sep, 16:30 - 16:55, Aula Contini
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