Compatible valuations and generalized Milnor 𝐾-theory

Efrat, Ido

doi:10.1090/S0002-9947-07-04132-3

Compatible valuations and generalized Milnor $K$-theory
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Trans. Amer. Math. Soc. 359 (2007), 4695-4709 Request permission

Abstract:

Given a field $F$ and a subgroup $S$ of $F^{\times }$ there is a minimal group $S\leq H_{S}\leq F^{\times }$ 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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