Timeline for Chern classes generating cohomology
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2010 at 12:14 | comment | added | Donu Arapura | Your question looks fine now, I removed my initial comments. | |
| Nov 16, 2010 at 4:24 | answer | added | roy smith | timeline score: 6 | |
| Nov 16, 2010 at 2:28 | comment | added | Donu Arapura | I unfortunately don't have time to write a complete answer to your edited last question, hopefully someone else will. The key point is that the cycle map from the Chow group $CH(X)\otimes Q\to H^(X)$ can be identified with the Chern character of $K(X)\otimes Q$. | |
| Nov 16, 2010 at 2:26 | history | edited | Vamsi | CC BY-SA 2.5 |
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| Nov 16, 2010 at 2:11 | history | edited | Vamsi | CC BY-SA 2.5 |
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| Nov 16, 2010 at 2:05 | comment | added | Donu Arapura | Yes, the last statement is equivalent to the Hodge conjecture. Sorry if my joke seemed at your expense. It's interesting that you arrived at the conjecture in this way. You might still want to edit the first sentence. It sounds almost like you are asserting something which isn't true. Non-Hodge classes won't be spanned by Chern classes. | |
| Nov 16, 2010 at 1:35 | comment | added | Vamsi | I am sorry (I phrased the question wrongly). I edited my question. I mean why is the Hodge conjecture equivalent to "Rational cohomology is generated by Chern classes of holomorphic vector bundles". | |
| Nov 16, 2010 at 1:32 | history | edited | Vamsi | CC BY-SA 2.5 |
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| Nov 16, 2010 at 0:29 | history | asked | Vamsi | CC BY-SA 2.5 |