The groups of points on abelian varieties over finite fields

Rybakov, Sergey

doi:10.48550/arxiv.0903.0106

Cited by 3 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper we classify ℓ-torsion of abelian varieties in two cases: when the Weil polynomial is separable, and for abelian surfaces. This result is similar to the classification of groups of k-points A(k) (see [Ry10]). These two problems are closely related, but the former one seems to be easier.…”

Section: Introductionsupporting

confidence: 85%

Finite group subschemes of abelian varieties over finite fields

Rybakov¹

2014

Finite Fields and Their Applications

Self Cite

View full text Add to dashboard Cite

Let A be an abelian variety over a finite field k. The k-isogeny class of A is uniquely determined by the Weil polynomial f A . We assume that f A is separable. For a given prime number ℓ = char k we give a classification of group schemes B[ℓ], where B runs through the isogeny class, in terms of certain Newton polygons associated to f A . As an application we classify zeta functions of Kummer surfaces over k.

show abstract

Section: Introductionsupporting

confidence: 85%

Finite group subschemes of abelian varieties over finite fields

Rybakov¹

2014

Finite Fields and Their Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recall some definitions and results from [Ry10]. For an abelian group G we denote by G ℓ the ℓ-primary component of G. The group A(k) is a kernel of 1 − F : A → A, and the ℓ-component [Ry10,Proposition 3.1]). The proof of the following lemma is essentially the proof of [Ry10, Theorem 1.1].…”

Section: Resultsmentioning

confidence: 99%

“…Xing partly classified groups of points on supersingular surfaces in [Xi94] and in [Xi96]. In the paper [Ry10] we show that one could use the language of Hodge polygons to describe groups of points. Moreover, we classify this groups for abelian varieties with commutative endomorphism algebra.…”

Section: Introductionmentioning

confidence: 99%

The groups of points on abelian surfaces over finite fields

Rybakov¹

2012

Contemporary Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this paper we state some partial results concerning higher dimensions. In particular, we prove a conjecture stated in [Ry10]. We also clarify the proof of the classification theorem for groups of points on abelian surfaces.…”

Section: Introductionmentioning

confidence: 84%