The absolute galois group of subfields of the field of totally S-ADIC numbers

Dan Haran, Moshe Jarden, Florian Pop

Research output: Contribution to journalArticlepeer-review

Abstract

For a finite set S of local primes of a countable Hilbertian field K and for δ1; δe 2 Gal(K) we denote the field of totally S-Adic numbers by Ktot;S, the fixed field of δ1; δe in Ktot;S by Ktot;S(δ), and the maximal Galois extension of K in Ktot;S(δ) by Ktot;S[δ]. We prove that for almost all δ € Gal(K)e the absolute Galois group of Ktot;S[δ] is isomorphic to the free product of Fω and a free product of local factors over S.

Original languageEnglish
Pages (from-to)205-223
Number of pages19
JournalFunctiones et Approximatio, Commentarii Mathematici
Volume46
Issue number2
DOIs
StatePublished - 2012

Keywords

  • Absolute Galois Group
  • Free Product
  • Haar measure
  • Hilbertian field
  • Local Primes
  • Totally S-Adic numbers

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