An observation on the cyclicity of the group of the \(\mathbb F_p\)-rational points of Abelian surfaces

DOI10.1007/BF03167542zbMath1155.14032OpenAlexW1514133369MaRDI QIDQ957696

Takuya Yamauchi

Publication date: 1 December 2008

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167542

zbMATH Keywords

densityabelian surfacereduction mod p

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Finite ground fields in algebraic geometry (14G15) Arithmetic ground fields for abelian varieties (14K15)

Cites Work

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• On Artin's conjecture
• Division fields of \(Y^ 2=X^ 3-aX\)
• Cyclicity and generation of points mod \(p\) on elliptic curves
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Quelques applications du théorème de densité de Chebotarev
• On the cyclicity of the group of \({\mathbb F}_p\)-rational points of non-CM elliptic curves
• Reductions of an elliptic curve and their Tate-Shafarevich groups
• Good reduction of abelian varieties
• Galois properties of points of finite order of elliptic curves
• Cyclicity of CM elliptic curves modulo 𝑝
• Explicit Determination of the Images of the Galois Representations Attached to Abelian Surfaces with End(A) = Z
• On Artin's conjecture.

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