Galois Extensions of Hilbertian Fields
نویسنده
چکیده
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 ∈ G(K)e, the field Ks[ ] ∩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 = T p∈S T σ∈G(K) K σ p . G(K) stands for the absolute Galois group of K. For each = (σ1, . . . , σe) ∈ G(K)e we denote the fixed field of σ1, . . . , σe in Ks by Ks( ). The maximal Galois extension of K in Ks( ) is Ks[ ]. Finally “almost all” means “for all but a set of Haar measure zero”.
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