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Automorphisms of two-dimensional quadrics

Alexandr Zaitsev

Abstract

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.

Automorphisms of two-dimensional quadrics

Abstract

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.
Paper Structure (6 sections, 35 theorems, 108 equations)

This paper contains 6 sections, 35 theorems, 108 equations.

Table of Contents

  1. Introduction
  2. Jordan constants and group theory
  3. Semidirect products
  4. Jordan constants of a group $\text{Aut}(\mathbb{P}^1_K \times \mathbb{P}^1_K)$
  5. Jordan constants of groups of type $\mathop{\rm PGL}\nolimits_2(L) \rtimes \mathbb{Z}/2\mathbb{Z}$
  6. Computation of $M(K)$

Key Result

Theorem 1.2

Let $K$ be a field of characteristic $0$.

Theorems & Definitions (67)

  • Definition 1.1: Pop
  • Theorem 1.2
  • Corollary 1.3
  • Theorem 1.4
  • Example 1.5
  • Proposition 1.6
  • Lemma 2.1
  • Lemma 2.2: see for example Pop
  • Definition 2.3
  • Theorem 2.4: see for example Isaacs
  • ...and 57 more