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I am a Postdoc in mathematics at the Shanghai Jiao Tong 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
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...