Duke Mathematical Journal

The negative K-theory of normal surfaces

Charles Weibel

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Abstract

We relate the negative $K$-theory of a normal surface to a resolution of singularities. The only nonzero $K$-groups are $K\sb {-2}$, which counts loops in the exceptional fiber, and $K\sb {-1}$, which is related to the divisor class groups of the complete local rings at the singularities. We also verify two conjectures of Srinivas about $K\sb 0$-regularity and $K\sb {-1}$ of a surface.

Article information

Source
Duke Math. J. Volume 108, Number 1 (2001), 1-35.

Dates
First available: 5 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1091737123

Mathematical Reviews number (MathSciNet)
MR1831819

Digital Object Identifier
doi:10.1215/S0012-7094-01-10811-9

Zentralblatt MATH identifier
01820813

Subjects
Primary: 14C35: Applications of methods of algebraic $K$-theory [See also 19Exx]
Secondary: 13C20: Class groups [See also 11R29] 19E08: $K$-theory of schemes [See also 14C35]

Citation

Weibel, Charles. The negative K -theory of normal surfaces. Duke Mathematical Journal 108 (2001), no. 1, 1--35. doi:10.1215/S0012-7094-01-10811-9. http://projecteuclid.org/euclid.dmj/1091737123.


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