Milnor K-theory of smooth varieties
نویسنده
چکیده
Let k be a field and X a smooth projective variety of dimension d over k. Generalizing a construction of Kato and Somekawa, we define a Milnortype group Ks(k; CH0(X);Gm) which is isomorphic to the ordinary Milnor K-group Km s (k) in the case X = Spec k. We prove that Ks(k; CH0(X);Gm) is isomorphic to both the higher Chow group CHd+s(X, s) and the Zariski cohomology group Hd Zar(X,K d+s).
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