Subgroup Structure of Fundamental Groups in Positive Characteristic

Lior Bary-Soroker*, Manish Kumar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let Π be the étale fundamental group of a smooth affine curve over an algebraically closed field of characteristic p > 0. We establish a criterion for profinite freeness of closed subgroups of Π. Roughly speaking, if a closed subgroup of Π is "captured" between two normal subgroups, then it is free, provided it contains most of the open subgroups of index p. In the proof we establish a strong version of "almost ω-freeness" of Π and then apply the Haran-Shapiro induction.

Original languageEnglish
Pages (from-to)3705-3719
Number of pages15
JournalCommunications in Algebra
Volume41
Issue number10
DOIs
StatePublished - Oct 2013

Funding

FundersFunder number
Lion Foundation

    Keywords

    • Diamond theorems
    • Free groups
    • Fundamental groups
    • Normal subgroups

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