Timeline for comparing Hodge structures on cohomology of conjugate varieties
Current License: CC BY-SA 3.0
12 events
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| Aug 16, 2012 at 14:29 | comment | added | Damian Rössler | In case you are still interested, the standard conjectures imply the following $$ {\rm dim}_{\bf Q}(H^a(X,\Omega^a)\cap H^{2a}(X({\bf C}),{\bf Q}))= {\rm dim}_{\bf Q}(H^a(X_\sigma,\Omega^a)\cap H^{2a}(X_\sigma({\bf C}),{\bf Q})) $$ for any $\sigma\in{\rm Aut}({\bf C})$ and $a\geq 0$. | |
| Aug 13, 2012 at 12:18 | vote | accept | o a | ||
| Aug 13, 2012 at 7:40 | comment | added | Damian Rössler | In this context, you might be interested in the notion of "absolute Hodge cycle", introduced by Deligne in his article "Hodge cycles on abelian varieties" (notes by J. Milne). | |
| Aug 12, 2012 at 16:47 | answer | added | Donu Arapura | timeline score: 9 | |
| Aug 12, 2012 at 15:55 | comment | added | Will Sawin | They are because they are the dimension of algebraically defined vector spaces. | |
| Aug 12, 2012 at 15:43 | history | edited | o a | CC BY-SA 3.0 |
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| Aug 12, 2012 at 15:29 | comment | added | o a | Will Sawin: what does it mean 'the structure factors through the automorphism' $\sigma$ ; in what sense ? Then I am still confused whether Hodge numbers are preserved... | |
| Aug 12, 2012 at 15:09 | history | edited | o a | CC BY-SA 3.0 |
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| Aug 12, 2012 at 15:04 | comment | added | o a | maybe this is just a confusion/silliness on my part, I admit... | |
| Aug 12, 2012 at 15:04 | comment | added | o a | Jason Starr: what is the answer to that part ? Do you mean to say that $dim_C H^a(X,Ω^b_X)$ is a definition of these numbers in algebraic de Rham cohomology ? | |
| Aug 12, 2012 at 14:33 | comment | added | Jason Starr | I think you should reconsider your first question, "For example ..." (the answer is very easy). | |
| Aug 12, 2012 at 14:24 | history | asked | o a | CC BY-SA 3.0 |