Let R be any ring with identity. We show that the homotopy category of all acyclic chain
complexes of pure-projective R-modules is a compactly generated triangulated category …

Let R be a Noetherian ring and I an ideal generated by a regular sequence. The category of
I-adically complete R-modules is not Abelian, but it can be enlarged to an Abelian category …

Let R be a commutative Noetherian ring. We introduce the notion of localization functors λ W
with cosupports in arbitrary subsets W of Spec R; it is a common generalization of …

We introduce a tensor compatibility condition for t-structures. For any Noetherian scheme X,
we prove that there is a one-to-one correspondence between the set of Thomason filtrations …

Let R be a ring and Q be a quiver. We study the homotopy categories K (PrjQ) and K (InjQ)
consisting, respectively, of projective and injective representations of Q by R-modules. We …

It is well-known that Grothendieck categories need not have projective objects (eg [12],
18.12). However, projective objects can be obtained from certain finiteness conditions. By a …

Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors γ
W with supports in arbitrary subsets W of Spec R. If W is a specialization-closed subset, then …

Here a topological R-left module. Y is called topologically coherent if it admits a basis of
neighborhoods of 0 consisting of submodules X'such that-X/S'is coherent in the category of …

Self-dual t-structure Page 1 Publ. RIMS Kyoto Univ. 52 (2016), 271–295 DOI 10.4171/PRIMS/181
Self-dual t-structure by Masaki Kashiwara Abstract We give a self-dual t-structure on the …

We explore the interplay between t‐structures in the bounded derived category of finitely
presented modules and the unbounded derived category of all modules over a coherent ring …