Bounds for the order for p-elementary subgroups in the plane Cremona group over a perfect field

TL;DR

This paper establishes a precise upper limit for the size of p-elementary subgroups within the plane Cremona group over any perfect field, advancing understanding of its subgroup structure.

Contribution

It provides a sharp bound for p-elementary subgroups in the plane Cremona group over perfect fields, a novel result in algebraic geometry.

Findings

Established a sharp bound for p-elementary subgroups

Applied the bound to classify subgroup structures

Extended results to arbitrary perfect fields

Abstract

We obtain a sharp bound for p-elementary subgroups in the plane Cremona group over an arbitrary perfect field.