Notes on the quasi-galois closed schemes

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.

5 pages

References in corpus (6)

• Automorphism Groups of Quasi-galois Closed Arithmetic Schemes
• On the existence of geometric models for function fields in several variables
• On the arithmetic fundamental groups
• On the étale fundamental groups of arithmetic schemes, revised
• Affine Structures on a Ringed Space and Schemes
• On the algebraic fundamental groups

Cited by in corpus (3)

• On the section conjecture of Grothendieck
• Algebraic Anabelian Functors
• Notes on the section conjecture of Grothendieck