On the étale fundamental groups of arithmetic schemes, revised

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.

Revised. 23 pages

References in corpus (5)

• 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 algebraic fundamental groups
• On the unramified extension of an arithmetic function field in several variables

Cited by in corpus (6)

• On the algebraic fundamental groups
• Notes on the quasi-galois closed schemes
• On the section conjecture of Grothendieck
• On the unramified extension of an arithmetic function field in several variables
• On the arithmetic Galois covers of higher relative dimensions
• Algebraic Anabelian Functors