Signature morphisms from the Cremona group over a non-closed field

Stéphane Lamy (1) , Susanna Zimmermann (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove that the plane Cremona group over a perfect field with at least one Galois extension of degree 8 is a non-trivial amalgam, and that it admits a surjective morphism to a free product of groups of order two.

Domaines: Géométrie algébrique [math.AG]; Théorie des groupes [math.GR]

Stéphane Lamy, Susanna Zimmermann. Signature morphisms from the Cremona group over a non-closed field. Journal of the European Mathematical Society, 2020, ⟨10.4171/JEMS/983⟩. ⟨hal-01719067⟩