On the arithmetic fundamental groups
Algebraic Geometry
2009-12-21 v2 Number Theory
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.
Cite
@article{arxiv.0910.0605,
title = {On the arithmetic fundamental groups},
author = {Feng-Wen An},
journal= {arXiv preprint arXiv:0910.0605},
year = {2009}
}
Comments
14 pages. Made changes in: convention 1.1; section 1.2; Definition 1.1; Remark 1.2