Estimates for the number of rational points on simple abelian varieties over finite fields

DOI10.1007/s00209-020-02520-wzbMath1479.11102arXiv1906.02264OpenAlexW3013416652MaRDI QIDQ2223517

Boris Kadets

Publication date: 29 January 2021

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

Full work available at URL: https://arxiv.org/abs/1906.02264

zbMATH Keywords

finite fieldsabelian varietiesnumber of rational points

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Varieties over finite and local fields (11G25)

Related Items (3)

Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽₂, 𝔽₃ and 𝔽₅ ⋮ Explicit methods in number theory. Abstracts from the workshop held July 18--24, 2021 (hybrid meeting) ⋮ Every positive integer is the order of an ordinary abelian variety over \(\mathbb{F}_2\)

Cites Work

• Computational excursions in analysis and number theory
• THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS
• Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
• Abelian varieties over finite fields
• On the number of points on abelian and Jacobian varieties over finite fields
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