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14 votes
2 answers
1k views

Is Deligne cohomology the motivic cohomology of analytic spaces?

Let $X$ be a smooth projective complex analytic space. We can cook up a complex analytic version of Bloch's cycle complex by declaring $z^n(X^{\rm an}, m)$ is the free abelian group on all ...
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12 votes
3 answers
2k views

Motivic vs Deligne cohomology

Where can I find the construction of the cycle class map from motivic cohomology to Deligne cohomology of smooth projective varieties over the complex numbers? It should be a construction by Bloch ...
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9 votes
0 answers
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Beilinson regulators and Bloch's mythological algebraic intermediate Jacobians

In the paper introducing his motivic cycle complexes, Bloch outlines a project he says he was going to return to in the future: Towards the end of page 270, he says, given a smooth projective variety ...
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