The cyclic homology and K K -theory of curves
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It is now possible to calculate the K-theory of a large class of singular curves over fields of characteristic zero. Roughly speaking, the K-theory of a curve is the K-theory of its (smooth) normalization plus a few shifted copies of the K-theory of the field plus a nil part. The nil part is a vector space depending only on the analytic type of the singularities, and may be computed locally. We completely compute the nil part for seminormal curves and give a conjectural calculation in general which depends upon cyclic homology. 1986 American Mathematical Society.