1 citations · 2 across the 13 of their papers we have counts for
13 papers
Krull--Gabriel dimension and Cohen-Macaulay representations
Naoya Hiramatsu, Yuji Yoshino
Let be a complete Cohen--Macaulay local ring and an -order. We study the Krull--Gabriel dimension of the functor category , wher…
Homological properties and finiteness of reducing invariants
Tokuji Araya, Naoya Hiramatsu, Ryo Takahashi
We study reducing invariants of modules related to certain homological properties. For modules of finite reducing projective dimension, we establish grade inequalities. We prove th…
A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes
Naoya Hiramatsu, Yuki Mifune, Ryo Takahashi
Let be a commutative noetherian ring, and let be a semidualizing -module. In this paper, we study levels of bounded complexes of finitely generated -modules with resp…
The spectrum of a category of maximal Cohen-Macaulay modules
Naoya Hiramatsu
We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay modules over a complete Cohen-Macaulay local ring. We define a topology on the space of isomorphism classe…
Krull--Gabriel dimension of Cohen--Macaulay modules over hypersurfaces of countable Cohen--Macaulay representation type
Naoya Hiramatsu
We calculate the Krull--Gabriel dimension of the functor category of the (stable) category of maximal Cohen--Macaulay modules over hypersurfaces of countable Cohen--Macaulay repres…
Geometry of varieties for graded maximal Cohen--Macaulay modules
Naoya Hiramatsu
We study a variety for graded maximal Cohen--Macaulay modules, which was introduced by Dao and Shipman. The main result of this paper asserts that there are only a finite number of…
A topology on the set of isomorphism classes of maximal Cohen--Macaulay modules
Naoya Hiramatsu, Ryo Takahashi
In this paper, we introduce a topology on the set of isomorphism classes of finitely generated modules over an associative algebra. Then we focus on the relative topology on the se…
Degenerations over -singularities and construction of degenerations over commutative rings
Naoya Hiramatsu, Ryo Takahashi, Yuji Yoshino
We give a necessary condition of degeneration via matrix representations, and consider degenerations of indecomposable Cohen-Macaulay modules over hypersurface singularities of typ…
Relations for Grothendieck groups of Gorenstein rings
Naoya Hiramatsu
We consider the converse of the Butler, Auslander-Reiten's Theorem which is on the relations for Grothendieck groups. We show that a Gorenstein ring is of finite representation typ…
On the stable hom relation and stable degenerations of Cohen-Macaulay modules
Naoya Hiramatsu
We study the stable hom relation for Cohen-Macaulay modules over Gorenstein local algebras. We give the sufficient condition to make the stable hom relation a partial order when th…
Degenerations of graded Cohen-Macaulay modules
Naoya Hiramatsu
We introduce a notion of degenerations of graded modules. In relation to it, we also introduce several partial orders as graded analogies of the hom order, the degeneration order a…
Remarks on subcategories of artinian modules
Naoya Hiramatsu
We study two subcategories of the category of artinian modules, a wide subcategory and a Serre subcategory. We prove that all wide subcategories of artinian modules are Serre subca…
Examples of degenerations of Cohen-Macaulay modules
Naoya Hiramatsu, Yuji Yoshino
We study the degeneration problem for maximal Cohen-Macaulay modules and give several examples of such degenerations. It is proved that such degenerations over an even-dimensional…