On the arithmetic fundamental groups

Abstract

In this paper we will define a qc fundamental group for an arithmetic scheme by quasi-galois closed covers. Then we will give a computation for such a group and will prove that the etale fundamental group of an arithmetic scheme is a normal subgroup in our qc fundamental group, which make up the main theorem of the paper. Hence, our group gives us a prior estimate of the etale fundamental group. The quotient group reflects the topological properties of the scheme.

14 pages. Made changes in: convention 1.1; section 1.2; Definition 1.1; Remark 1.2

References in corpus (4)

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

Cited by in corpus (8)

• Automorphism Groups of Quasi-galois Closed Arithmetic Schemes
• On the étale fundamental groups of arithmetic schemes, revised
• On the algebraic fundamental groups
• On the etale fundamental groups of arithmetic schemes
• Notes on the quasi-galois closed schemes
• On the section conjecture of Grothendieck
• Notes on the section conjecture of Grothendieck
• Algebraic Anabelian Functors