11 papers
On Takahashi's descent question about dominant local rings
Jian Liu
This article studies dominant local rings, a notion introduced by Takahashi. We prove that, for a flat local homomorphism R-->S between commutative noetherian local rings, dominanc…
Pretriangulated categories failing (TR4)
Xiao-Wu Chen, Jian Liu, Sergei O. Ivanov +3
We introduce gemstones in a pretriangulated category, which are used to perturb pretriangulated structures. For a triangulated category whose stable category of cohere…
Khovanov homology: pro-tangles, derived colimits and spectral sequences
Jian Liu, Kefeng Liu, Li Shen
This paper introduces \emph{pro-tangles}, a natural generalization of classical tangles, which are functors from the Boolean cube to Bar-Natan's cobordism category. By employing th…
Cotorsion pairs, thick subcategories, and finitely generated Gorenstein projective modules
Souvik Dey, Jian Liu, Xue-Song Lu
Let be a noetherian algebra over a Cohen--Macaulay ring admitting a canonical module , and assume that is maximal Cohen--Macaulay over . We prove that the categor…
Multi-scale symmetry analysis in molecular structures
Jing-Wen Gao, Yunan He, Jian Liu
Topological data analysis (TDA), as a relatively recent approach, has demonstrated great potential in capturing the intrinsic and robust structural features of complex data. While…
On local rings of finite syzygy representation type
Souvik Dey, Kaito Kimura, Jian Liu +1
Let be a commutative Noetherian local ring. We characterize when its completion has an isolated singularity, thereby strengthening the Dao-Takahashi refinement of the Auslander…
Base change of (Gorenstein) transpose, k-torsionfree modules, and quasi-faithfully flat extensions
Jian Liu
Let be a finite ring homomorphism, where is a two-sided Noetherian ring, and let be a finitely generated left -module. Under suitable homologic…
Openness with respect to levels in triangulated categories
Souvik Dey, Jian Liu, Liran Shaul
Given a compactly generated triangulated category equipped with an action of a graded-commutative Noetherian ring , generalizing results of Letz, we prove a genera…
Generation of singularity categories and infinite injective dimension locus via annihilation of cohomologies
Souvik Dey, Jian Liu, Yuki Mifune +1
Let R be a commutative Noetherian ring. We establish a close relationship between the strong generation of the singularity category of R and the nonvanishing of the annihilator of…
Classifying thick subcategories over a Koszul complex via the curved BGG correspondence
Jian Liu, Josh Pollitz
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…
The subdivision of hypergraphs
Jian Liu, Ran Liu, Jie Wu
Hypergraphs, as a generalization of simplicial complexes, have long been a subject of interest in their geometric interpretation. The subdivision of simplicial complexes can, to so…