Zobrazeno 1 - 10
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pro vyhledávání: '"Kimura, Kaito"'
Autor:
Kimura, Kaito
Let $R$ be a commutative Noetherian ring of dimension $d$. In this paper, we first show that some power of the cohomology annihilator annihilates the $(d+1)$-th Ext modules for all finitely generated modules when either $R$ admits a dualizing complex
Externí odkaz:
http://arxiv.org/abs/2409.17934
Autor:
Kimura, Kaito
Let $R$ be a Cohen-Macaulay local ring. In this paper, we first describe the radicals of annihilators of stable categories of maximal Cohen-Macaulay $R$-modules. We then prove that the Alexandrov topology of the stable category of maximal Cohen-Macau
Externí odkaz:
http://arxiv.org/abs/2401.04987
This paper provides a method to get a noetherian equicharacteristic local UFD with an isolated singularity from a given noetherian complete equicharacteristic local ring, preserving certain properties. This is applied to invesitgate the (non)vanishin
Externí odkaz:
http://arxiv.org/abs/2310.16599
Autor:
Kimura, Kaito
Let $R$ be a commutative noetherian ring, $I$ an ideal of $R$, and $M$ a finitely generated $R$-module. We consider the asymptotic injective dimensions, projective dimensions, Bass numbers, and Betti numbers of localizations of $M/I^n M$ at prime ide
Externí odkaz:
http://arxiv.org/abs/2310.11697
Autor:
Kimura, Kaito
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 main results of this paper asserts that the Auslander--Reiten conjectur
Externí odkaz:
http://arxiv.org/abs/2304.03956
Autor:
Kimura, Kaito
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 subject in commutative algebra. The main result of this paper asserts th
Externí odkaz:
http://arxiv.org/abs/2207.07807
Autor:
Kimura, Kaito
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, MCM, (S_n), and (T_n). One of the main results asserts that FID-loci
Externí odkaz:
http://arxiv.org/abs/2201.11955
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 modules. One of the applications shows that the Auslander-Reiten conjectu
Externí odkaz:
http://arxiv.org/abs/2106.08583