1 citations · 2 across the 12 of their papers we have counts for
15 papers · 1 filter
On some problems concerning the growth of Betti numbers
Kaito Kimura
We investigate several problems concerning the growth of Betti numbers over commutative noetherian rings. First, we establish uniform positive lower and finite upper bounds for the…
On injective dimension of the conormal module
Mohsen Gheibi, Kaito Kimura
Let be a Gorenstein local ring, let be a proper ideal of , and set . We investigate when finite injective dimension of the conormal module forces to b…
On strongly G-regular rings
Kaito Kimura, Yuki Mifune, Yuya Otake +1
A noetherian ring is called G-regular when all finitely generated Gorenstein projective modules are projective. In this paper, we study rings satisfying the stronger condition that…
Complexes of finite Gorenstein flat and injective dimensions
Kaito Kimura
In this paper, we consider a Gorenstein-dimensional analogue of Foxby's characterization of Gorenstein rings. We prove that a commutative Noetherian local ring is Gorenstein if it…
Trace ideals of canonical modules over Schubert cycles and determinantal rings
Kaito Kimura
In this paper, we study the canonical trace of Schubert cycles and determinantal rings. As an application, we give an explicit description of the non-Gorenstein locus and show that…
Finiteness of homological dimensions of Ext modules
Kaito Kimura
Let be a commutative Noetherian local ring and let and be nonzero finitely generated -modules. In this paper, we investigate how the finiteness of the homological di…
On the depth of tensor products over Cohen-Macaulay rings
Kaito Kimura, Justin Lyle, Andrew J. Soto-Levins
Inspired by classical work on the depth formula for tensor products of finitely generated -modules, we introduce two conditions which we call and $(\mathbf{rde…
Stability of annihilators of cohomology and closed subsets defined by Jacobian ideals
Kaito Kimura
Let be a commutative Noetherian ring of dimension . In this paper, we first show that some power of the cohomology annihilator annihilates the -th Ext modules for all…
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…
Openness of various loci over Noetherian rings
Kaito Kimura
In this paper, we consider the openness of the P-locus of a finitely generated module over a commutative noetherian ring in the case where P is each of the properties FID, Gor, CM,…
Maximal Cohen-Macaulay tensor products and vanishing of Ext modules
Kaito Kimura, Yuya Otake, Ryo Takahashi
In this paper, we investigate the maximal Cohen-Macaulay property of tensor products of modules, and then give criteria for projectivity of modules in terms of vanishing of Ext mod…