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Compatible valuations and generalized Milnor -theory
Authors:Ido Efrat
Affiliation:Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Be'er-Sheva 84105, Israel
Abstract:Given a field $ F$ and a subgroup $ S$ of $ F^{times }$ there is a minimal group $ Sleq H_{S}leq F^{times }$ for which there exists an $ S$-compatible valuation whose units are contained in $ H_{S}$. Assuming that $ S$ has finite index in $ F^{times }$ and contains $ (F^{times })^{p}$ for $ p$ prime, we describe $ H_{S}$ in computable $ K$-theoretic terms.

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