Products and polarizations of super-isolated abelian varieties

DOI10.1007/s00209-021-02791-xzbMath1498.11152arXiv2008.05738OpenAlexW3174216422MaRDI QIDQ2070939

Stefano Marseglia, Travis Scholl

Publication date: 25 January 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.05738

zbMATH Keywords

isogeny classpolarized isomorphismssuper-isolated abelian varieties

Mathematics Subject Classification ID

Isogeny (14K02) Varieties over finite and local fields (11G25) Algebraic numbers; rings of algebraic integers (11R04)

Uses Software

• Magma
• SageMath

Cites Work

• The Magma algebra system. I: The user language
• Some effective cases of the Brauer-Siegel theorem
• Constructing distinct curves with isomorphic Jacobians
• Categories of abelian varieties over finite fields. I: Abelian varieties over \(\mathbb F_p\)
• Super-isolated abelian varieties
• Computing abelian varieties over finite fields isogenous to a power
• Endomorphisms of Abelian varieties over finite fields
• Variétés abeliennes ordinaires sur un corps fini
• Isogeny classes of abelian varieties over finite fields
• On Resultants
• A REMARK ON ENDOMORPHISMS OF ABELIAN VARIETIES OVER FUNCTION FIELDS OF FINITE CHARACTERISTIC
• Principally Polarized Ordinary Abelian Varieties Over Finite Fields
• Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography
• Computing square-free polarized abelian varieties over finite fields
• New methods for bounding the number of points on curves over finite fields
• Abelian Surfaces over Finite Fields as Jacobians
• Number fields
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