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Results tagged with hodge-theory
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user 43108
The study of harmonic differential forms on complex projective varieties, their invariantly defined filtrations, their integrals over topological cycles, especially over subvarieties, the deformations of these integrals and filtrations in families, and a multitude of generalizations.
5
votes
Hodge standard conjecture in positive characteristic
Probably too late, but...
(1) Not quite. The Hodge index theorem only works for $\mathbb{C}$. To extend it to all characteristic $0$ ground fields, you need the Lefschetz principle and the comparison …
- 17.6k
14
votes
Accepted
Hodge standard conjecture for étale cohomology
I'm very interested myself on a better answer to this question, but let me point out the obvious: the main problem is that there is no Hodge theory on positive characteristic.
The proof in characteri …
- 17.6k
11
votes
Accepted
On Grothendieck's idea on his Standard Conjecture B
My guess is that he was thinking about crystalline cohomology.
It fits rather nicely in Grothendieck research at that time. He had obviously in mind the success of Dwork's p-adic approach to the Weil …
- 17.6k