Codimension 2
From Mathematics
(→The dilog in physics) |
(→Cycles in codim 2) |
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One would like to have that it factors through <math>CH^2(X) </math> and establishes that the morphism <math>H^2(X, K_2) \rightarrow CH^2(X)</math> is an ''isomorphism''. | One would like to have that it factors through <math>CH^2(X) </math> and establishes that the morphism <math>H^2(X, K_2) \rightarrow CH^2(X)</math> is an ''isomorphism''. | ||
| − | However, at this point, Bloch's article is a bit out-of-date. Quillen later proved by using the '''Gersten resolution''' of the sheaf <math>K_n^M(\mathcal{O}_X)</math> (Sheafified higher Milnor K-groups, cf. talk 5) that <math>H^n(X, K_n) \rightarrow CH^n(X)</math>. In the end one could say a couple of words on this (Reference: ) | + | However, at this point, Bloch's article is a bit out-of-date. Quillen later proved by using the '''Gersten resolution''' of the sheaf <math>K_n^M(\mathcal{O}_X)</math> (Sheafified higher Milnor K-groups, cf. talk 5) that <math>H^n(X, K_n^M) \rightarrow CH^n(X)</math>. In the end one could say a couple of words on this (Reference: ) |
References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) | References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) | ||
