4 papers · 1 filter
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…
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…
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…
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…