Derived length of zero entropy groups acting on projective varieties in arbitrary characteristic -- A remark to a paper of Dinh-Oguiso-Zhang

Abstract

Let $X$ be a projective variety of dimension $n\ge 1$ over an algebraically closed field of arbitrary characteristic. We prove a Fujiki-Lieberman type theorem on the structure of the automorphism group of $X$. Let $G$ be a group of zero entropy automorphisms of $X$ and $G_0$ the set of elements in $G$ which are isotopic to the identity. We show that after replacing $G$ by a suitable finite-index subgroup, $G/G_0$ is a unipotent group of the derived length at most $n-1$. This result was first proved by Dinh, Oguiso and Zhang for compact Kähler manifolds.

arXiv comment10 pages,comments are welcome! Accepted by International Journal of Mathematics

References in corpus (3)

• Jordan property for non-linear algebraic groups and projective varieties
• Some structure theorems for algebraic groups
• Compact Kähler manifolds admitting large solvable groups of automorphisms

Cited by in corpus (1)

• Wild automorphisms of projective varieties, the maps which have no invariant proper subsets