Vol. 8, No. 5, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Polarization estimates for abelian varieties

David Masser and Gisbert Wüstholz

Vol. 8 (2014), No. 5, 1045–1070
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.

Keywords
abelian varieties, estimating polarizations
Mathematical Subject Classification 2010
Primary: 11G10
Secondary: 11J95
Milestones
Received: 22 April 2013
Revised: 13 December 2013
Accepted: 15 February 2014
Published: 16 September 2014
Authors
David Masser
Mathematisches Institut
Universität Basel
CH-4051 Basel
Switzerland
Gisbert Wüstholz
Departement für Mathematik
ETH-Zentrum
CH-8092 Zürich
Switzerland