On the arithmetic fundamental groups

Details On the arithmetic fundamental groups On the arithmetic fundamental groups

2009-10-04

arxiv.org/abs/0910.0605v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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