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Compatible valuations and generalized Milnor -theory

Authors:	Ido Efrat

Institution:	Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Be'er-Sheva 84105, Israel

Abstract:	Given a field and a subgroup of $F^{\times }$ there is a minimal group $S\leq H_{S}\leq F^{\times }$ for which there exists an -compatible valuation whose units are contained in $H_{S}$ . Assuming that has finite index in $F^{\times }$ and contains $(F^{\times })^{p}$ for prime, we describe $H_{S}$ in computable -theoretic terms.

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