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## Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

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