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Results tagged with hodge-theory
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user 43054
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.
15
votes
Accepted
How to think about infinite generatedness of motivic cohomology
While waiting for someone more competent than me to answer, let me turn the question right back to you. Why should motivic cohomology be finitely generated?
The answer is, of course, that there's no …
- 16.5k
11
votes
Accepted
How to think about $\mathbf{Z}(n)_{\mathcal{M}}$
[All cohomology will be reduced cohomology for ease of notation].
There is no analog for classical homotopy theory. This is related to the fact that the Picard group of the category of spectra is $\m …
- 16.5k
7
votes
Accepted
A systematic canonical construction of the Hodge star operator
The first step is to construct a pairing on the modules $\bigwedge^k M$. I will assume that the pairing $g:M\otimes M\to R$ is perfect, that is it induces an isomorphism $M\to \textrm{Hom}(M,R)$. Then …
- 16.5k