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Torsion hypersurfaces on abelian schemes and Betti coordinates

Corvaja, Pietro and Masser, David and Zannier, Umberto. (2017) Torsion hypersurfaces on abelian schemes and Betti coordinates.

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Abstract

In this paper we extend to arbitrary complex coefficients certain finiteness results on Unlikely intersections linked to torsion in abelian surface schemes over a curve, which have been recently proved for the case of algebraic coefficients; in this way we complete the solution of Zilber-Pink conjecture for abelian surface schemes over a curve. As experience has shown also in previous cases, the extension from algebraic to complex coefficients often requires entirely new arguments, whereas simple specialization arguments fail.
The outcome gives as a byproduct new finiteness results when the base of the scheme has arbitrary dimension; another consequence is a proof of an expectation of Mazur concerning the structure of the locus in the base when a given section is torsion. Finally, we show the link with an old work of Griffiths and Harris on a higher dimensional extension of a theorem of Poncelet.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Masser, David
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:17 Apr 2019 20:44
Deposited On:28 Mar 2019 09:51

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