Compatible valuations and generalized Milnor 𝐾-theory

Efrat, Ido

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

Compatible valuations and generalized Milnor $K$-theory

Author: Ido Efrat
Journal: Trans. Amer. Math. Soc. 359 (2007), 4695-4709
MSC (2000): Primary 19F99; Secondary 12J15, 19C99, 12J99
DOI: https://doi.org/10.1090/S0002-9947-07-04132-3
Published electronically: April 24, 2007
MathSciNet review: 2320647
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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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