Rationality of the quotient of $\mathbb{P}^2$ by finite group of   automorphisms over arbitrary field of characteristic zero
  Let $\Bbbk$ be a field of characteristic zero and $G$ be a finite group of automorphisms of projective plane over $\Bbbk$. Castelnuovo's criterion implies that the quotient of projective plane by $G$ is rational if the field $\Bbbk$ is algebraically closed. In this paper we prove that $\mathbb{P}^2_{\Bbbk} / G$ is rational for an arbitrary field $\Bbbk$ of characteristic zero. 
Andrey S. Trepalin
math.AG