6 papers · 1 filter
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…