We construct the Chow ringCH*(X) =CH0(X)⊕CH1(X)⊕CH2(X) of a reduced, quasi-projective surfaceX, together with Chern class mapsci :K0(X) → CHi(X), with the usual properties. As a consequence, we show that the cycle mapCH2(X)→ F0K0(X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine’s, but is much simpler, since we deal only with surfaces.
Volume 130, 2020
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