9 papers · 1 filter
Ranks of Verdier quotients of derived categories over local rings
Souvik Dey, Yuki Mifune
Let be a commutative noetherian local ring with residue field . Denote by the bounded derived category of finitely generated -modules. In…
Orlov's functors in Macaulay2
Michael K. Brown, Souvik Dey, Geoffrey Fatin +3
Given a commutative and graded Gorenstein ring with associated projective variety , a theorem of Orlov gives fully faithful embeddings from the graded singularity category o…
On Partial Trace Ideals
Souvik Dey, Shinya Kumashiro
We investigate the notion of partial trace ideals, recently introduced by Maitra. We first establish several properties of partial trace ideals and give affirmative answers to ques…
Centers of Endomorphism Rings and Reflexivity
Souvik Dey, Justin Lyle
Let be a local ring and let be a finitely generated -module. Appealing to the natural left module structure of over its endomorphism ring and corresponding center $Z…
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…
Extremal behavior of ideals of minors
Trung Chau, Michael DeBellevue, Souvik Dey +2
Let be either a fiber product or an artinian stretched Gorenstein ring, with in the latter case. We prove that the…
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…
Upper bounds for dimensions of singularity categories and their annihilators
Souvik Dey, Yuki Mifune
Let be a commutative noetherian ring. Denote by the category of finitely generated -modules and by the bounded derived categor…