Geodesic
Projectivity of the Absolute Galois Groups of Multi-Valued Fields
Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 28-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article, we establish the projectivity property for the enriched Galois groups of multi-valued fields having a near Boolean family of valuation rings and satisfying the arithmetic local-global principle $\mathrm{LG}_A$. This property extends the corresponding property that was proved by the author for the case of Boolean families. As application, we give a sufficient condition for the inverse Galois problem to be solvable. This condition can be applied in particular to the wonderful extensions of the field of rational numbers. 
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Yu. L. Ershov. Projectivity of the Absolute Galois Groups of Multi-Valued Fields. Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 28-33. http://geodesic.mathdoc.fr/item/MT_2003_6_1_a1/

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