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Compactness of the Alexandrov topology of maximal Cohen-Macaulay modules
Kaito Kimura
Let be a Cohen-Macaulay local ring. In this paper, we first describe the radicals of annihilators of stable categories of maximal Cohen-Macaulay -modules. We then prove that…
On the vanishing of Ext modules over a local unique factorization domain with an isolated singularity
Kaito Kimura, Justin Lyle, Yuya Otake +1
This paper provides a method to get a noetherian equicharacteristic local UFD with an isolated singularity from a given noetherian complete equicharacteristic local ring, preservin…
Asymptotic behavior of homological invariants of localizations of modules
Kaito Kimura
Let be a commutative noetherian ring, an ideal of , and a finitely generated -module. We consider the asymptotic injective dimensions, projective dimensions, Bass…
Auslander--Reiten conjecture for normal rings
Kaito Kimura
In this paper, sufficient conditions for finitely generated modules over a commutative noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the m…
Asymptotic stability of depths of localizations of modules
Kaito Kimura
Let R be a commutative noetherian ring, I an ideal of R, and M a finitely generated R-module. The asymptotic behavior of the quotient modules M/I^n M of M is an actively studied su…