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” …

Derived categories and equivalences between them are the pièce de résistance of modern
homological algebra. They are widely used in many branches of mathematics, especially in …

A new method is established to construct recollements of derived categories of rings from
exact contexts and noncommutative tensor products. This method is applicable to a large …

We introduce the notion of big tilting complexes over associative rings, which is a
simultaneous generalization of good tilting modules and tilting complexes over rings. Given …

We introduce symmetric subcategories of abelian categories and show that the derived
category of the endomorphism ring of any good tilting module over a ring is a recollement of …

Let U be a dg-A-module, B the endomorphism dg-algebra of U. We know that if U is a good
silting object, then there exist a dg-algebra C and a recollement among the derived …

Exact contexts and their noncommutative tensor products are introduced which generalize
the notions of Milnor squares and usual tensor products over commutative rings …

Let $ U $ be a silting object in a derived category over a dg-algebra $ A $, and let $ B $ be
the endomorphism dg-algebra of $ U $. Under some appropriate hypotheses, we show that …

We introduce a new concept of s-recollements of extriangulated categories, which
generalizes recollements of abelian categories, recollements of triangulated categories, as …

As is known, derived categories (or more generally, triangulated categories) and derived
equivalences, introduced by Grothendieck and Verdier in [57], have connections with many …