On the arithmetic fundamental groups

2009/10/04 by Feng-Wen An, An, Feng-Wen
Mathematics · #11G35 #14F35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0910.0605

openalex publication_date 2009/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

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