PSC Galois extensions of Hilbertian fields

Wulf Dieter Geyer*, Moshe Jarden

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove the following result: Theorem. Let K be a countable Hilbertian field, S a finite set of local primes of K, and e ≥ 0 an integer. Then, for almost all σ ∈ G(K)e, the field Ks[σ] ∩ Ktot,S is PSC. Here a local prime is an equivalent class p of absolute values of K whose completion is a local field, K̂p. Then Kp = Ks ∩ K̂p and Ktot,S = ∩ p∈Sσ∈G KpΣ. G(K) stands for the absolute Galois group of K. For each σ = (σ1,..., σe) ∈ G(K)e we denote the fixed field of σ1,..., σe in Ks by Ks (σ). The maximal Galois extension of K in Ks (σ) is Ks[σ]. Finally "almost all" means "for all but a set of Haar measure zero".

Original languageEnglish
Pages (from-to)119-160
Number of pages42
JournalMathematische Nachrichten
StatePublished - 2002


  • Hilbertian fields
  • Pseudo-S-closed
  • Rumeley existence theorem
  • Stable fields


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