The cyclic homology and K-theory of curves
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.
Algebraic K-theory, Cyclic homology, Singular curve
Geller, S., L. Reid, and C. Weibel. "The cyclic homology and $ K $-theory of curves." Bulletin (New Series) of the American Mathematical Society 15, no. 2 (1986): 205-208.
Bulletin of the American Mathematical Society