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Polarization Estimates for Abelian Varieties

Masser, David and Wüstholz, Gisbert. (2014) Polarization Estimates for Abelian Varieties. Preprints Fachbereich Mathematik, 2014 (16).

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Abstract

In an earlier paper we showed that an abelian variety over a number field of fixed degree has a polarization whose degree is bounded by a power of its logarithmic Faltings height, provided there are only trivial endomorphisms. Here we greatly relax the endomorphism hypothesis, and we even eliminate it completely when the dimension is at most seven. Our methods ultimately go back to transcendence theory, with the asymmetric geometry of numbers as a new ingredient, together with what we call the Severi-Néron group, a variant of the Néron-Severi group.
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:12 May 2019 23:15
Deposited On:28 Mar 2019 09:52

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