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

TL;DR

This paper demonstrates that the plane Cremona group over certain perfect fields is a non-trivial amalgam and can be mapped onto a free product of groups of order two, revealing new structural properties.

Contribution

It establishes the non-trivial amalgam structure of the Cremona group over fields with specific Galois extensions and constructs a surjective morphism to a free product of order-two groups.

Findings

Cremona group over such fields is a non-trivial amalgam.

Existence of a surjective morphism to a free product of groups of order two.

New insights into the algebraic structure of Cremona groups over non-closed fields.

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.