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math.AC2025
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…
math.AC2025
An approach to Martsinkovsky's invariant via Auslander's approximation theory
Yuya Otake
Auslander developed a theory of the -invariant for finitely generated modules over commutative Gorenstein local rings, and Martsinkovsky extended this theory to the -invarian…
math.AC2025
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…