Relations in the Cremona group over perfect fields

Abstract

For perfect fields $k$ satisfying $[\bar{k}:k]>2$, we construct new normal subgroups of the plane Cremona group and provide an elementary proof of its non-simplicity, following the melody of the recent proof by Blanc, Lamy and Zimmermann that the Cremona group of rank $n$ over (subfields of) the complex numbers is not simple for $n\ge 3$.

to appear in Annales de l'Institut Fourier