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Relatively Projective Groups as Absolute Galois Groups

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Progress in Galois Theory

Part of the book series: Developments in Mathematics ((DEVM,volume 12))

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Abstract

A group structure G = (G, G l,..., G n) is projective if and only if G is isomorphic to a Galois group structure

$$ Gal(K) = (Gal(K),Gal(K_1 ),...,Gal(K_n ))$$

of a field-valuation structure K = (K,K l,v 1,...,,K n,v n) where (K i,v i) is the Henselian closure of (K, v i|K) and K is pseudo closed with respect to K l,...,K n.

Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation.

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Haran, D., Jarden, M. (2005). Relatively Projective Groups as Absolute Galois Groups. In: Voelklein, H., Shaska, T. (eds) Progress in Galois Theory. Developments in Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-23534-5_5

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