P-adically projective groups as absolute Galois groups

Let F be a finite set of classical local fields of characteristic 0 which is closed under Galois isomorphism and let G be a profinite group. Then G is isomorphic to the absolute Galois group of a P FC field K if and only if G is F-projective and Subgr(G,Gal(F)) is strictly closed in Subgr(G) for eac...

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Bibliographic Details
Published in:International Mathematics Research Notices 2005-01, Vol.2005 (32), p.1957-1995
Main Authors: Haran, Dan, Jarden, Moshe, Pop, Florian
Format: Article
Language:English
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Summary:Let F be a finite set of classical local fields of characteristic 0 which is closed under Galois isomorphism and let G be a profinite group. Then G is isomorphic to the absolute Galois group of a P FC field K if and only if G is F-projective and Subgr(G,Gal(F)) is strictly closed in Subgr(G) for each F ∈ F. Moreover, given G as above, K is equipped with a set of valuations satisfying the block approximation theorem.
ISSN:1073-7928
1687-1197
1687-0247
DOI:10.1155/IMRN.2005.1957