非交换霍奇猜想

IF 0.7 2区数学 Q2 MATHEMATICS Journal of Noncommutative Geometry Pub Date : 2021-02-06 DOI:10.4171/jncg/517

Xun Lin

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引用次数: 3

摘要

本文给出了$\3\dg$类的有理Hodge猜想的一个版本。非交换霍奇猜想等价于\cite{perry2020integral}中提出的关于可容许子范畴的版本。我们用非交换几何的方法得到了霍奇猜想的证据实例。最后，我们证明了光滑固有连接$\3\dg$代数的非交换Hodge猜想是成立的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Noncommutative Hodge conjecture

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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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.