Codimension 2
From Mathematics
(→Cycles in codim 2) |
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* Explain that (via resolutions of the structure sheaf of codimension 2 subvarieties by vector bundles) one gets a map | * Explain that (via resolutions of the structure sheaf of codimension 2 subvarieties by vector bundles) one gets a map | ||
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| + | <math> \{\text{codim 2 subvarieties}\} \rightarrow H^2(X, K_2)</math> | ||
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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''. | ||
| + | However, at this point, Bloch's article is a bit out-of-date.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(\mathcal{O}_X)</math> 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: ) | ||
References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) | References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) | ||
