On the étale fundamental groups of arithmetic schemes, revised

2009/10/26 by Feng-Wen An, An, Feng-Wen · 2 citations
Mathematics · #11G35 #14F35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0910.4646

openalex publication_date 2009/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we will give a computation of the étale fundamental group of an integral arithmetic scheme. For such a scheme, we will prove that the étale fundamental group is naturally isomorphic to the Galois group of the maximal formally unramified extension over the function field. It consists of the main theorem of the paper. Here, formally unramified will be proved to be arithmetically unramified which is defined in an evident manner and coincides with that in algebraic number theory. Hence, formally unramified has an arithmetic sense. At the same time, such a computation coincides with the known result for a normal noetherian scheme.

Citations

• Automorphism Groups of Quasi-galois Closed Arithmetic Schemes
• On the existence of geometric models for function fields in several variables

Cited by

• On the algebraic fundamental groups
• Notes on the quasi-galois closed schemes

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