arXiv subjects
Publications and source records attributed to Alexandr Zaitsev.
We prove that the group of birational automorphisms of a geometrically irreducible algebraic surface over a finite field is Jordan. We show that the analogous statement fails in higher dimensions. Finally, we prove that groups of birational permutations over finite fields have bounded finite $p'$-subgroups; in particular, they are $p$-Jordan.
We give an explicit bound on orders of finite subgroups of Cremona group of rank three over $\mathbb{Q}$.
In this paper we compute the Jordan constants of the Cremona group of rank two over all fields of characteristic zero.
In this paper, we find the maximum values that the Jordan constant of the automorphism group of a smooth two-dimensional rational quadric over a field of characteristic zero can attain, depending on the arithmetic properties of a field.
In this paper we obtain necessary and sufficient condition for existence of del Pezzo surfaces of degree $5$ and $6$ over a field $K$ with a prescribed action of absolute Galois group $\text{Gal} ( K^{\text{sep}}/K)$ on the graph of $(-1)$-curves. Also we compute automorphism groups of del Pezzo surfaces of degree $5$ over arbitrary fields.