14 citations · 23 across the 8 of their papers we have counts for
9 papers
Indecomposable pure-injective objects in stable categories of Gorenstein-projective modules over Gorenstein orders
Tsutomu Nakamura
We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules over a complete Gorenstein order. In particular, we prove that a complete Gorenstein order is…
Tilting complexes and codimension functions over commutative noetherian rings
Michal Hrbek, Tsutomu Nakamura, Jan Šťovíček
In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the "slice"…
Flat cotorsion modules over Noether algebras
Ryo Kanda, Tsutomu Nakamura
For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalizatio…
Telescope conjecture for homotopically smashing t-structures over commutative noetherian rings
Michal Hrbek, Tsutomu Nakamura
We show that any homotopically smashing t-structure in the derived category of a commutative noetherian ring is compactly generated. This generalizes the validity of the telescope…
Minimal semi-flat-cotorsion replacements and cosupport
Tsutomu Nakamura, Peder Thompson
Over a commutative noetherian ring of finite Krull dimension, we show that every complex of flat cotorsion -modules decomposes as a direct sum of a minimal complex and a con…
Little dimension and the improved new intersection theorem
Tsutomu Nakamura, Ryo Takahashi, Siamak Yassemi
Let be a commutative noetherian local ring. We define a new invariant for -modules which we call the little dimension. Using it, we extend the improved new intersection theo…
Cosupports and minimal pure-injective resolutions of affine rings
Tsutomu Nakamura
We prove that any affine ring over a field has full cosupport, i.e., the cosupport of is equal to . Using this fact, we give a complete description of a…
Localization functors and cosupport in derived categories of commutative Noetherian rings
Tsutomu Nakamura, Yuji Yoshino
Let be a commutative Noetherian ring. We introduce the notion of localization functors with cosupports in arbitrary subsets of ; it is a common gener…
A local duality principle in derived categories of commutative Noetherian rings
Tsutomu Nakamura, Yuji Yoshino
Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors with supports in arbitrary subsets of Spec R, which is a natural generalization of right…