The absolute Galois group of a pseudo real closed field with finitely many orders
The author gives a characterization of the absolute Galois group G(K) of a prc-field K which admits exactly e orderings (prc e-field). A field K is called prc if each K-variety which has a simple point in every real closure of K, admits a K-rational point. The author assigns to every field K with e orderings a so-called absolute Galois e-structure \({\mathcal G}(K)\) and proves that in the category of profinite e-structures the ones which are realized by prc e-fields are exactly the projective ones. A profinite e-structure is a system \({\mathcal G}=(G\); \(X_ 1,...,X_ e)\) where G is a profinite group and the \(X_ i's\) are non-empty G-orbits such that the group \(\{\) \(\tau\in G|\) \(x^{\tau}=x\}\) is cyclic of order 2. After introducing morphisms suitably, the notion of projectivity is defined as usual.
scientific article; zbMATH DE number 3957248
scientific article