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

Abstract

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.

Statements only over perfect fields instead of arbitrary fields (see Remark 1.3). A few other minor corrections

Cited by in corpus (4)

• Quotients of higher dimensional Cremona groups
• Algebraic subgroups of the plane Cremona group over a perfect field
• Generating the plane Cremona groups by involutions
• The real plane Cremona group is a non-trivial amalgam