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2014 Polarization estimates for abelian varieties
David Masser, Gisbert Wüstholz
Algebra Number Theory 8(5): 1045-1070 (2014). DOI: 10.2140/ant.2014.8.1045

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.

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David Masser. Gisbert Wüstholz. "Polarization estimates for abelian varieties." Algebra Number Theory 8 (5) 1045 - 1070, 2014. https://doi.org/10.2140/ant.2014.8.1045

Information

Received: 22 April 2013; Revised: 13 December 2013; Accepted: 15 February 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1311.11051
MathSciNet: MR3263135
Digital Object Identifier: 10.2140/ant.2014.8.1045

Subjects:
Primary: 11G10
Secondary: 11J95

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.8 • No. 5 • 2014
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