Notes on the quasi-galois closed schemes

2009/11/05 by Feng-Wen An, An, Feng-Wen
Mathematics · #14H30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #msc:14H30

paper · pdf · doi:10.48550/arxiv.0911.1073

5 pages

openalex publication_date 2009/11/05 · arxiv created 2009/12/20 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f:X→ 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.

Citations

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

Related

• Automorphism Groups of Quasi-galois Closed Arithmetic Schemes
• The Conjugates of Algebraic Schemes
• The inverse Galois problem for connected algebraic groups
• The determination of integral closures and geometric applications
• Fundamental groups of proper varieties are finitely presented