Almost locally free fields

作者：Jarden Moshe^*

来源：Journal of Algebra, 2011, 335(1): 171-176.

DOI：10.1016/j.jalgebra.2011.03.021

• Galois group
• Abhyankar's conjecture
• omega-free groups
• Embedding problems

Using the positive solution of the general Abhyankar's conjecture, we prove that the fundamental group pi(1)(C) of the smooth connected affine curve C is "almost free". That is, for each positive integer e and for almost all sigma =(sigma(1), ... ,sigma(e)) epsilon pi(1) (C)(e) in the sense of the Haar measure, the closed subgroup of pi(1) (C) generated by sigma(1), ... ,sigma(e) is profinite free on e generators. This implies a theorem of Harbat

• 出版日期2011-6-1