Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Unexpected subgroup schemes of PGL_{2,k} in characteristic 2

Bianca Gouthier, Dajano Tossici

Abstract

If the characteristic of a field $k$ is odd any infinitesimal group scheme of $PGL_{2,k}$ lifts to $SL_{2,k}$. In this paper, we prove that this is not true in characteristic $2$ and we give a complete description, up to isomorphism, of infinitesimal unipotent subgroup schemes of $PGL_{2,k}$. Also, the infinitesimal trigonalizable case is considered.

Unexpected subgroup schemes of PGL_{2,k} in characteristic 2

Abstract

If the characteristic of a field is odd any infinitesimal group scheme of lifts to . In this paper, we prove that this is not true in characteristic and we give a complete description, up to isomorphism, of infinitesimal unipotent subgroup schemes of . Also, the infinitesimal trigonalizable case is considered.
Paper Structure (6 sections, 12 theorems, 39 equations)

This paper contains 6 sections, 12 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. Infinitesimal subgroup schemes of $\operatorname{PGL}_{2,k}$ in characteristic $p>2$
  3. Infinitesimal unipotent subgroups schemes of $\operatorname{GL}_{2,k}$
  4. Some noncommutative unipotent infinitesimal group schemes.
  5. Proof of the Theorem
  6. Actions of trigonalizable group schemes over $\mathbb{P}^1_k$

Key Result

Theorem 1.1

Let $k$ be a field of characteristic $2$.

Theorems & Definitions (25)

  • Theorem 1.1
  • Corollary 1.2
  • Lemma 2.1
  • proof
  • Proposition 2.2
  • proof
  • Proposition 3.1
  • proof
  • Definition 4.1
  • Lemma 4.2
  • ...and 15 more