The groups of points on abelian varieties over finite fields

DOI10.2478/s11533-010-0003-xzbMath1198.14043arXiv0903.0106OpenAlexW2079508602MaRDI QIDQ708003

Sergey Yu. Rybakov

Publication date: 8 October 2010

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.0106

zbMATH Keywords

abelian varietyWeil polynomial

Mathematics Subject Classification ID

Rational points (14G05) Finite ground fields in algebraic geometry (14G15) Arithmetic ground fields for abelian varieties (14K15)

Related Items (9)

Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽₂, 𝔽₃ and 𝔽₅ ⋮ On the cyclicity of the rational points group of abelian varieties over finite fields ⋮ Groups of points on abelian threefolds over finite fields ⋮ On some categories of structured sets ⋮ Varieties over finite fields: quantitative theory ⋮ Finite group subschemes of abelian varieties over finite fields ⋮ Local cyclicity of isogeny classes of abelian varieties defined over finite fields ⋮ Cyclic abelian varieties over finite fields in ordinary isogeny classes ⋮ Abelian surfaces over finite fields with prescribed groups

Cites Work

• Nonsingular plane cubic curves over finite fields
• The structure of the rational point groups of simple abelian varieties of dimension two over finite fields
• On supersingular abelian varieties of dimension two over finite fields
• Lectures on \(p\)-divisible groups
• A Note on Elliptic Curves Over Finite Fields
• Notes on Crystalline Cohomology. (MN-21)
• A note on elliptic curves over finite fields
• Abelian varieties over finite fields
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