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arXiv · 2102.03481

Noncommutative Hodge conjecture

Xun Lin
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Abstract

The paper provides a version of the rational Hodge conjecture for $\3\dg$ categories. The noncommutative Hodge conjecture is equivalent to the version proposed in \cite{perry2020integral} for admissible subcategories. We obtain examples of evidence of the Hodge conjecture by techniques of noncommutative geometry. Finally, we show that the noncommutative Hodge conjecture for smooth proper connective $\3\dg$ algebras is true.

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Xun Lin. 2021-02-06. Noncommutative Hodge conjecture. https://arxiv.org/abs/2102.03481

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