5 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…
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…