Polarization estimates for abelian varieties

Gisbert Wüstholz, David Masser

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1045-1070
JournalAlgebra & Number Theory
Issue number5
Publication statusPublished - 2014

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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