On elements of order p^s in the plane Cremona group over a field of characteristic p

TL;DR

This paper investigates the structure of the plane Cremona group over fields of characteristic p, establishing bounds on the orders of its elements and classifying certain conjugacy classes, revealing limitations on p-power order elements.

Contribution

It proves that the Cremona group over characteristic p fields lacks elements of order p^s for s > 1 except when p=2, and classifies conjugacy classes of elements of order 4.

Findings

No elements of order p^s for s > 1 unless p=2

Elements of order 4 are classified into conjugacy classes

The group does not contain elements of order p^2 unless p=2

Abstract

We show that the plane Cremona group over a field of characteristic p > 0 does not contain elements of order of power of p larger than 2 and it does not contain elements of order p^2 unless p =2. Also we describe conjugacy classes of elements of order 4.