Non simplicit\'e du groupe de Cremona sur tout corps

TL;DR

This paper proves that the Cremona group in two dimensions is not simple over any field by demonstrating the existence of elements satisfying a weakened WPD property, extending previous results to all fields.

Contribution

It establishes the non-simplicity of the 2D Cremona group over any field using a novel application of a theorem by Dahmani, Guirardel, and Osin.

Findings

Cremona group in 2D is not simple over any field

Existence of elements with a weakened WPD property in the group

Connection to Bestvina and Fujiwara's property

Abstract

Using a theorem of Dahmani, Guirardel and Osin we prove that the Cremona group in 2 dimension is not simple, over any field. More precisely, we show that some elements of this group satisfy a weakened WPD property which is equivalent in our particular context to the Bestvina and Fujiwara's one.