3 papers
math.AG2026
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 surface. As an application, w…
math.AG2025
Lattices in Tate modules
Bjorn Poonen, Sergey Rybakov
Refining a theorem of Zarhin, we prove that given a -dimensional abelian variety and an endomorphism of , there exists a matrix $A \in \operatorname{M}_{2g}(\mathbb{Z…
math.AG2025
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…