Signature morphisms from the Cremona group
Also appears in collection : French-German meeting on complex algebraic geometry / Rencontre franco-allemande en géométrie algébrique complexe
The plane Cremona group is the group of birational transformations of the projective plane. I would like to discuss why over algebraically closed fields there are no homomorphisms from the plane Cremona group to a finite group, but for certain non-closed fields there are (in fact there are many). This is joint work with Stéphane Lamy.