The structure of the group of rational points of an abelian variety over a finite field

Springer, Caleb

doi:10.1007/s40879-021-00460-1

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2021

2022

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Cited by 2 publications

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“…Rybakov provided classification results for the group of points in [Ryb10] and [Ryb15] in terms of the Newton polygon of the characteristic polynomial of Frobenius. The second author gave a classification in terms of the endomorphism ring of the abelian variety in [Spr21].…”

Section: Introductionmentioning

confidence: 99%

Every finite abelian group is the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$

Marseglia¹,

Springer²

2021

Preprint

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Section: Introductionmentioning

confidence: 99%

Every finite abelian group is the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$

Marseglia¹,

Springer²

2021

Preprint

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Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽₂, 𝔽₃ and 𝔽₅

Marseglia

Springer

2022

Proc. Amer. Math. Soc.

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We show that every finite abelian group occurs as the group of rational points of an ordinary abelian variety over F 2 \mathbb {F}_2 , F 3 \mathbb {F}_3 and F 5 \mathbb {F}_5 . We produce partial results for abelian varieties over a general finite field F q \mathbb {F}_q . In particular, we show that certain abelian groups cannot occur as groups of rational points of abelian varieties over F q \mathbb {F}_q when q q is large. Finally, we show that every finite cyclic group arises as the group of rational points of infinitely many simple abelian varieties over F 2 \mathbb {F}_2 .

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The structure of the group of rational points of an abelian variety over a finite field

Cited by 2 publications

References 15 publications

Every finite abelian group is the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$

Every finite abelian group is the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$

Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽₂, 𝔽₃ and 𝔽₅

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