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Projective extensions of fields

Abstract:

Every field K admits proper projective extensions, that is, Galois extensions where the Galois group is a non-trivial projective group, unless K is separably closed or K is a Pythagorean formally real field without cyclic extensions of odd degree. As a consequence, it turns out that almost all absolute Galois groups decompose as proper semidirect products. We show that each local field has a unique maximal projective extension, and that the same holds for each global field of positive charact...

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Publication status:
Published

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Publisher copy:
10.1112/S0024610706022678

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume:
73
Issue:
3
Pages:
639-656
Publication date:
2006-06-05
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
URN:
uuid:7aadc8d0-5f78-4d3e-ab22-11e93519cb9f
Source identifiers:
24028
Local pid:
pubs:24028
Language:
English

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