We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general context of the model theory of fields with a (finite) group scheme action.

中文翻译：

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具有有限群作用的存在闭域

我们研究具有固定有限群作用的存在封闭场的代数和模型理论性质。在相当强烈的意义上，这些场被证明是伪代数封闭的。我们将这项工作置于具有（有限）群方案作用的场模型理论的更一般背景下。