TY - JOUR
T1 - PSC Galois extensions of Hilbertian fields
AU - Geyer, Wulf Dieter
AU - Jarden, Moshe
PY - 2002
Y1 - 2002
N2 - 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∈S ∩σ∈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".
AB - 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∈S ∩σ∈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".
KW - Hilbertian fields
KW - Pseudo-S-closed
KW - Rumeley existence theorem
KW - Stable fields
UR - http://www.scopus.com/inward/record.url?scp=0036312712&partnerID=8YFLogxK
U2 - 10.1002/1522-2616(200203)236:1<119::AID-MANA119>3.0.CO;2-U
DO - 10.1002/1522-2616(200203)236:1<119::AID-MANA119>3.0.CO;2-U
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AN - SCOPUS:0036312712
SN - 0025-584X
VL - 236
SP - 119
EP - 160
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
ER -