60 citations · 291 across the 64 of their papers we have counts for
6 papers · 2 filters
Hochster's theta pairing and numerical equivalence
Hailong Dao, Kazuhiko Kurano
Let $(A,\m)$ be a local hypersurface with isolated singularity. We show that Hochster's theta pairing vanishes on elements that are {numerically equivalent to zero} in the Grothend…
Modules that detect finite homological dimensions
Olgur Celikbas, Hailong Dao, Ryo Takahashi
We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a…
Non-commutative resolutions and Grothendieck groups
Hailong Dao, Osamu Iyama, Ryo Takahashi +1
Let be a noetherian normal domain. We investigate when admits a faithful module whose endomorphism ring has finite global dimension. This can be viewed as a non-commutative…
Upper bounds for dimensions of singularity categories
Hailong Dao, Ryo Takahashi
This paper gives upper bounds for the dimension of the singularity category of a Cohen-Macaulay local ring with an isolated singularity. One of them recovers an upper bound given b…
The dimension of a subcategory of modules
Hailong Dao, Ryo Takahashi
Let R be a commutative noetherian local ring. As an analogue of the notion of the dimension of a triangulated category defined by Rouquier, the notion of the dimension of a subcate…
Classification of resolving subcategories and grade consistent functions
Hailong Dao, Ryo Takahashi
We classify certain resolving subcategories of finitely generated modules over a commutative noetherian ring R by using integer-valued functions on Spec R. As an application we giv…