We study the behavior of direct limits in the heart of a t-structure. We prove that, for any
compactly generated t-structure in a triangulated category with coproducts, countable direct …

This memoir completes the series of papers beginning with [KL1, KL2], showing that, for a
commutative noetherian ring $\Lambda $, either the category of $\Lambda $-modules of …

We prove for a large family of rings R that their λ-pure global dimension is greater than one
for each infinite regular cardinal λ. This answers in the negative a problem posed by …

Several years ago, Bondal, Rouquier and Van den Bergh introduced the notion of the
dimension of a triangulated category, and Rouquier proved that the bounded derived …

We study when the heart of at-structure in a triangulated category D with coproducts is AB5
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …

In this paper we extend two results of Happel to commutative rings. Let $(A,\mathfrak {m}) $
be a commutative Noetherian local ring. Let $ D^ b_f (mod\A) $ be the bounded derived …

In [3] Jan-Eric Roos has shown that an abelian category 31 is a locally Noetherian
Grothendieck category if and only if (iff) it is dual to the category of complete (and Hausdorff) …

The aim of this paper is to unify classification theories of torsion classes of finite dimensional
algebras and commutative Noetherian rings. For a commutative Noetherian ring R and a …

In [TV], Bertrand To\" en and Michel Vaqui\'e define a scheme theory for a closed monoidal
category $(\mathcal {C},\otimes, 1) $. One of the key ingredients of this theory is the …

For a commutative noetherian ring A, we compare the support of a complex of A-modules
with the support of its cohomology. This leads to a classification of all full subcategories of A …