The cyclic homology and K K theory of curves
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It is now possible to calculate the Ktheory of a large class of singular curves over fields of characteristic zero. Roughly speaking, the Ktheory of a curve is the Ktheory of its (smooth) normalization plus a few shifted copies of the Ktheory 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.
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Geller, S., Reid, L., & Weibel, C.
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