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Notes on the quasi-galois closed schemes

Feng-Wen An
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Abstract

Let $f:X\to Y$ be a surjective morphism of integral schemes. Then $X$ is said to be quasi-galois closed over $Y$ by $f$ if $X$ has a unique conjugate over $Y$ in an algebraically closed field. Such a notion has been applied to the computation of étale fundamental groups. In this paper we will use affine coverings with values in a fixed field to discuss quasi-galois closed and then give a sufficient and essential condition for quasi-galois closed. Here, we will avoid using affine structures on a scheme since their definition looks copious and fussy.

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Feng-Wen An. 2009-12-20. Notes on the quasi-galois closed schemes. https://arxiv.org/abs/0911.1073

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