Projective pairs of profinite groups

Lior Bary-Soroker*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We generalize the notion of a projective profinite group to a projective pair of a profinite group and a closed subgroup.We establish a connection with Pseudo Algebraically Closed (PAC) extensions of PAC fields: Let M be an algebraic extension of a PAC field K. Then M/K is PAC if and only if the corresponding pair of absolute Galois groups (Gal(M),Gal(K)) is projective. Moreover any projective pair can be realized as absolute Galois groups of a PAC extension of a PAC field.Using this characterization we construct new examples of PAC extensions of relatively small fields, e.g. unbounded abelian extensions of the rational numbers.

Original languageEnglish
Pages (from-to)2112-2128
Number of pages17
JournalJournal of Algebra
Volume324
Issue number9
DOIs
StatePublished - Nov 2010
Externally publishedYes

Funding

FundersFunder number
Israel Science Foundation343/07

    Keywords

    • Embedding problem
    • PAC
    • Profinite group
    • Projective group
    • Pseudo algebraically closed

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