Levine, Marc; Weibel, Chuck Zero cycles and complete intersections on singular varieties. (English) Zbl 0555.14004 J. Reine Angew. Math. 359, 106-120 (1985). We construct a relative Chow group \(CH_ 0(X,Y)\) associated to a singular variety X with a closed subset Y containing the singular locus of X. This comes equipped with a cycle map \(\gamma: X-Y\to CH_ 0(X,Y),\) and our main geometric result is that the relation of rational equivalence is \(\sigma\)-closed. This is, \(\gamma^{-1}(0)\) is a countable union of closed subsets of X-Y. We apply this to the case in which \(X=Spec(A)\) is a singular affine surface and obtain our main algebraic result: the set of maximal ideals of A which are complete intersections is \(\sigma\)-closed in the set of all regular maximal ideals of A. Cited in 3 ReviewsCited in 19 Documents MSC: 14C25 Algebraic cycles 14M10 Complete intersections 14C05 Parametrization (Chow and Hilbert schemes) 14C15 (Equivariant) Chow groups and rings; motives 14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry 14B05 Singularities in algebraic geometry Keywords:\(K_ 0\); \(G_ 0\); relative Chow group; singular variety; rational equivalence; complete intersections PDF BibTeX XML Cite \textit{M. Levine} and \textit{C. Weibel}, J. Reine Angew. Math. 359, 106--120 (1985; Zbl 0555.14004) Full Text: Crelle EuDML OpenURL