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

2019/09/18 by Sichen Li, Li, Sichen
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14C25 #14G17 #14J50 #37B40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1909.08201

openalex publication_date 2019/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a projective variety of dimension n≥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 G₀ 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/G₀ 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.

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