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Mennicke symbols, $ K$-cohomology and a Bass-Kubota theorem


Author: J. Fasel
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
Published electronically: July 16, 2014
MathSciNet review: 3271257
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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.


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Additional Information

J. Fasel
Affiliation: Fakultät Mathematik, Universität Duisburg-Essen, Campus Essen, Thea-Leymann-Strasse 9, D-45127 Essen, Germany
Email: jean.fasel@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2014-06011-X
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
Article copyright: © Copyright 2014 American Mathematical Society

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