Compatible valuations and generalized Milnor $K$-theory
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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.References
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Additional Information
- Ido Efrat
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel
- Email: efrat@math.bgu.ac.il
- Received by editor(s): March 24, 2005
- Published electronically: April 24, 2007
- Additional Notes: This research was supported by the Israel Science Foundation grant No. 8008/02–1
- © Copyright 2007 American Mathematical Society
- 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
- MathSciNet review: 2320647