The negative K-theory of normal surfaces

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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.

Original languageEnglish (US)
Pages (from-to)1-35
Number of pages35
JournalDuke Mathematical Journal
Volume108
Issue number1
DOIs
StatePublished - Jan 1 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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