The Embedding Problem over a Hilbertian Pac-field
نویسنده
چکیده
We show that the absolute Galois group of a countable Hilbertian P(seudo)A(lgebraically)C(losed) field of characteristic 0 is a free profinite group of countably infinite rank (Theorem A). As a consequence, G(Q̄/Q) is the extension of groups with a fairly simple structure (e.g., ∏∞ n=2 Sn) by a countably free group. In addition, we characterize those PAC fields over which every finite group is a Galois group as those with the RG-Hilbertian property (Theorem B).
منابع مشابه
Almost Hilbertian Fields *
This paper is devoted to some variants of the Hilbert specialization property. For example, the RG-hilbertian property (for a field K), which arose in connection with the Inverse Galois Problem, requires that the specialization property holds solely for extensions of K(T ) that are Galois and regular over K. We show that fields inductively obtained from a real hilbertian field by adjoining real...
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