Mennicke symbols, $K$-cohomology and a Bass-Kubota theorem
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Abstract:
If $A$ is a smooth algebra of dimension $d\geq 3$ over a perfect field $k$ of characteristic different from $2$, then we show that the universal Mennicke symbol $MS_{d+1}(A)$ is isomorphic to the $K$-cohomology group $H^d(A,K_{d+1})$. We then prove an analogue of the Bass-Kubota theorem for smooth affine surfaces over the algebraic closure of a finite field.References
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Additional Information
- J. Fasel
- Affiliation: Fakultät Mathematik, Universität Duisburg-Essen, Campus Essen, Thea-Leymann-Strasse 9, D-45127 Essen, Germany
- MR Author ID: 824144
- Email: jean.fasel@gmail.com
- Received by editor(s): October 17, 2011
- Received by editor(s) in revised form: November 7, 2012
- Published electronically: July 16, 2014
- Additional Notes: The author was partially supported by the Swiss National Science Foundation, grant PAOOP2_129089
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 191-208
- MSC (2010): Primary 13C10, 14C25, 14C35, 19A13, 19B14, 19E20; Secondary 19G38
- DOI: https://doi.org/10.1090/S0002-9947-2014-06011-X
- MathSciNet review: 3271257