English

Noncommutative Hodge conjecture

Algebraic Geometry 2021-10-08 v3

Abstract

The paper provides a version of the rational Hodge conjecture for \3\dg\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\3\dg algebras is true.

Keywords

Cite

@article{arxiv.2102.03481,
  title  = {Noncommutative Hodge conjecture},
  author = {Xun Lin},
  journal= {arXiv preprint arXiv:2102.03481},
  year   = {2021}
}

Comments

A revised version. Fix a gap concerning the issue of splitting of Hodge filtration

R2 v1 2026-06-23T22:53:37.313Z