Algebraic subgroups of the plane Cremona group over a perfect field

TL;DR

This paper classifies all maximal algebraic subgroups of the plane Cremona group over a perfect field, showing that any infinite algebraic subgroup is contained within one of these maximal groups and classifying their rational point subgroups.

Contribution

It provides a complete classification of maximal algebraic subgroups of the plane Cremona group over a perfect field, including their conjugacy classes and rational points.

Findings

Every infinite algebraic subgroup is contained in a maximal one.

Maximal algebraic subgroups are classified up to conjugacy.

Subgroups of rational points are also classified.

Abstract

We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in a maximal algebraic subgroup of the plane Cremona group. We classify the maximal groups, and their subgroups of rational points, up to conjugacy by a birational map.