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The Higher K-Theory of a Complex Surface

Published online by Cambridge University Press:  04 December 2007

Claudio Pedrini  and
Charles Weibel
Claudio Pedrini
Affiliation:
DIMA – Università di Genova, Genova, Italy. E-mail: pedrinidima.unige.it
Charles Weibel
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ, U.S.A. E-mail: [email protected]
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Abstract

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Let X be a smooth complex variety of dimension at most two, and let F be its function field. We prove that the K-groups of F are divisible above the dimension of X, and that the K-groups of X are divisible-by-finite. We also describe the torsion in the K-groups of F and X.

Keywords

algebraic K-theorycomplex surfacehigher Chow groupsDeligne–Beilinson cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 129 , Issue 3 , December 2001 , pp. 239 - 271
Copyright
© 2001 Kluwer Academic Publishers