Jian Liu

Jian Liu
  • Ph.D. University of Science and Technology of China
  • Associate Research Fellow at Central China Normal University

About

15
Publications
650
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
34
Citations
Introduction
I am working in mathematics at the Central China Normal University. I finished my Ph.D. at the University of Science and Technology of China (September 2016-- June 2021). From August 2019 to October 2020, I visited the University of Utah. My advisors are Prof. Xiao-Wu Chen and Prof. Srikanth Iyengar. My research interests are derived categories, commutative algebras, and representation theory of finite dimensional algebras. Here is my homepage: https://jianliu.org
Current institution
Central China Normal University
Current position
  • Associate Research Fellow
Additional affiliations
July 2021 - June 2023
Shanghai Jiao Tong University
Position
  • Post doc
Education
August 2019 - October 2020
University of Utah
Field of study
  • Pure Mathematics, Algebra
September 2016 - June 2021
University of Science and Technology of China
Field of study
  • Pure Mathematics, Algebra
September 2013 - June 2016
Northeast Normal University
Field of study
  • Mathematics

Publications

Publications (15)
Article
Full-text available
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally complete intersection ring are self-dual under Grothendieck duality. This was proved by Stevenson when the ri...
Article
Full-text available
We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between the homotopy categories of acyclic complexes of injective modules. We give conditions on when a bimodule appear...
Article
Full-text available
Let R be a commutative Noetherian ring. We prove that if R is either an equidimensional finitely generated algebra over a perfect field, or an equidimensional equicharacteristic complete local ring with a perfect residue field, then the annihilator of the singularity category of R coincides with the Jacobian ideal of R up to radical. We establish a...
Preprint
Full-text available
Let $\varphi\colon R\rightarrow A$ be a ring homomorphism, where $R$ is a commutative noetherian ring and $A$ is a finite $R$-algebra. We give criteria for detecting the ascent and descent of Gorenstein homological properties. As an application, we get a result that supports a question of Avramov and Foxby. We observe that the ascent and descent of...
Preprint
Full-text available
Let R be a commutative Noetherian ring. We establish a close relationship between the (strong) generation of the singularity category of R, the nonvanishing of the annihilator of the singularity category of R, and the nonvanishing of the cohomological annihilator of modules. As an application, we prove that the singularity category of R has a stron...
Preprint
Full-text available
In this work we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously recovers a theorem of Stevenson when the list of elements is a regular sequence and the classification of thick subcategories for an exterior algebra over a field (via th...
Article
In this article a condition is given to detect the containment among thick subcategories of the bounded derived category of a commutative noetherian ring. More precisely, for a commutative noetherian ring R R and complexes of R R -modules with finitely generated homology M M and N N , we show N N is in the thick subcategory generated by M M if and...
Preprint
Full-text available
Let R be a commutative noetherian ring. We prove that if R is either an equidimensional finitely generated algebra over a perfect field, or an equidimensional equicharacteristic complete local ring with a perfect residue field, then the annihilator of the singularity category of R coincides with the Jacobian ideal of R up to radical. We establish a...
Preprint
Full-text available
We investigate the triangulated hull of the orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull will correspond to the full subcategory of compact objects of certain triangulated categories of periodic complexes. This spec...
Preprint
Full-text available
This work concerns surjective maps $\varphi\colon R\to S$ of commutative noetherian local rings with kernel generated by a regular sequence that is part of a minimal generating set for the maximal ideal of $R$. The main result provides criteria for detecting such exceptional complete intersection maps in terms of the lattices of thick subcategories...
Preprint
Full-text available
In this article a condition is given to detect the containment among thick subcategories of the bounded derived category of a commutative noetherian ring. More precisely, for a commutative noetherian ring $R$ and complexes of $R$-modules with finitely generated homology $M$ and $N$, we show $N$ is in the thick subcategory generated by $M$ if and on...
Preprint
Full-text available
We investigate the problem when the tensor functor by a bimodule yields a singular equivalence. It turns out that this problem is equivalent to the one when the Hom functor given by the same bimodule induces a triangle equivalence between the homotopy categories of acyclic complexes of injective modules. We give conditions on when a bimodule appear...
Preprint
Full-text available
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thick subcategories of the bounded derived category of a locally complete intersection ring are self-dual under Grothendieck duality. This was proved by Stevenson when the ri...

Network

Cited By