Codimension 2
From Mathematics
(→Cech cohomology and the Hodge conjecture in codim 1) |
(→Chow groups and Chern classes) |
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| Line 102: | Line 102: | ||
The classical construction of Chow groups and the Chern classes using the splitting principle. | The classical construction of Chow groups and the Chern classes using the splitting principle. | ||
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| + | * Classification of vector bundles by Cech-cocycles, Theorem 5.10<ref name="Wei13"/>. Mention also that for a projective complex algebraic variety <math>X</math>, complex analytic vector bundles, classified by <math>H^1(X^{an}, \mathcal{O}_X^{an})</math> (analytic Cech cohomology), are the same as algebraic vector bundles on <math>X</math>, classified by <math>H^1(X, \mathcal{O}_X)</math> (Zariski Cech cohomology). | ||
| + | * Splitting principle: Theorem 5.19<ref name="Wei13"/> | ||
| + | * Definition of Chern classes using this<ref name=""/> | ||
= Elementary algebraic K-Theory: K0 and K1 = | = Elementary algebraic K-Theory: K0 and K1 = | ||
