Non simplicité du groupe de Cremona sur tout corps

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.

In French. An English version is available on the webpage of the author

References in corpus (1)

• Some effectivity questions for plane Cremona transformations

Cited by in corpus (6)

• Random walks, WPD actions, and the Cremona group
• Relations in the Cremona group over perfect fields
• Acylindrical hyperbolicity of the three-dimensional tame automorphism group
• On the acylindrical hyperbolicity of the tame automorphism group of ${\mathrm{SL}}_2(\mathbb{C})$
• Combinatorics of the tame automorphism group
• The Abelianisation of the real Cremona group