# Jian LiuCentral China Normal University · Department of Mathematics

Jian Liu

Ph.D. University of Science and Technology of China

## About

13

Publications

505

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17

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

**Skills and Expertise**

Additional affiliations

July 2021 - June 2023

Education

August 2019 - October 2020

September 2016 - June 2021

September 2013 - June 2016

## Publications

Publications (13)

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...