S. Rybakov

activity

20092026

most citedThe groups of points on abelian varieties over finite fields

3 citations · 8 across the 11 of their papers we have counts for

collaborators

12 papers

math.AG2026

Twisted Deligne modules and abelian varieties over finite fields

Sergey Rybakov

Isogeny classes of abelian varieties over finite fields were described by Tate and Honda. Deligne proved that the category of ordinary abelian varieties over a finite field is equi…

math.AG2024

Generalized Kummer surfaces over finite fields

Sergey Rybakov

In this paper, we prove a refinement of the Katsura theorem on finite group actions on abelian surfaces such that the quotient is birational to a $K 3$ surface. As an application, w…

math.AG2024

Principal polarizations on products of abelian varieties over finite fields

Sergey Rybakov

We refine and generalize the results of K. E. Lauter and E. W. Howe on principal polarizations on products of abelian varieties over finite fields. Firstly, we study the reasons fo…

math.AG2021★ 2 cited

Lattices in Tate modules

Bjorn Poonen, Sergey Rybakov

Refining a theorem of Zarhin, we prove that given a $g$ -dimensional abelian variety $X$ and an endomorphism $u$ of $X$ , there exists a matrix $A \in \operatorname{M}_{2g}(\mathbb{Z…

math.AG2019

A family of K3 surfaces and towers of algebraic curves over finite fields

Sergey Galkin, Sergey Rybakov

For a family of K3 surfaces we implement a variation of a general construction of towers of algebraic curves over finite fields given in a previous paper. As a result we get a good…

math.AG2017

Families of algebraic varieties and towers of algebraic curves over finite fields

Sergey Rybakov

We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.

math.AG2016★ 1 cited

Minimal cubic surfaces over finite fields

Sergey Rybakov, Andrey Trepalin

Let $X$ be a minimal cubic surface over a finite field $F_{q}$ . The image $Γ$ of the Galois group $Gal (F_{q} / F_{q})$ in the group $…

math.AG2014

On classification of groups of points on abelian varieties over finite fields

Sergey Rybakov

In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polyno…

math.AG2013

DG-modules over de Rham DG-algebra

Sergey Rybakov

For a morphism of smooth schemes over a regular affine base we define functors of derived direct image and extraordinary inverse image on coderived categories of DG-modules over de…

math.AG2010

The groups of points on abelian surfaces over finite fields

Sergey Rybakov

Let $A$ be an abelian surface over a finite field $k$ . The $k$ -isogeny class of $A$ is uniquely determined by a Weil polynomial $f_{A}$ of degree 4. We give a classification of the g…

math.AG2010★ 2 cited

Finite group subschemes of abelian varieties over finite fields

Sergey Rybakov

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 gi…

math.AG2009★ 3 cited

The groups of points on abelian varieties over finite fields

Sergey Rybakov

Let $A$ be an abelian variety with commutative endomorphism algebra over a finite field $k$ . The $k$ -isogeny class of $A$ is uniquely determined by a Weil polynomial $f_{A}$ without…