Polarizations on abelian varieties

DOI10.1017/S0305004102005935zbMATH Open1011.14011arXivmath/0002253OpenAlexW2963670361MaRDI QIDQ4796069

Alice Silverberg, Yuri G. Zarhin

Publication date: 16 March 2003

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Abstract: The results in this paper imply that for every number field F and positive integer r, there exists an F-isogeny class of abelian varieties such that r divides the degree of every F-polarization on every abelian variety in the isogeny class.

Full work available at URL: https://arxiv.org/abs/math/0002253

zbMATH Keywords

abelian varietypolarizationisogenyprincipal polarization

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Isogeny (14K02)

Related Items (7)

DEGREES OF POLARIZATIONS ON AN ABELIAN SURFACE WITH REAL MULTIPLICATION ⋮ Unnamed Item ⋮ Polarisations of type \((1,2,\dots ,2)\) on abelian varieties ⋮ Higher syzygies on general polarized Abelian varieties of type (1,⋯,1,d)$(1,\dots ,1,d)$ ⋮ Points of small order on three-dimensional abelian varieties; with an appendix by Yuri Zarhin ⋮ Products and polarizations of super-isolated abelian varieties ⋮ On the universal abelian variety of dimension 4

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