Noncommutative Hodge conjecture

  • Xun Lin

    Tsinghua University, Beijing, China
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The paper provides a version of the rational Hodge conjecture for categories. The noncommutative Hodge conjecture is equivalent to the version proposed by Perry (2022) 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 algebras is true.

Cite this article

Xun Lin, Noncommutative Hodge conjecture. J. Noncommut. Geom. 17 (2023), no. 4, pp. 1367–1389

DOI 10.4171/JNCG/517