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” …

We introduce the notion of torsion-simple objects in an abelian category: these are the
objects which are always either torsion or torsion-free with respect to any torsion pair. We …

We show that Krause's recollement exists for any locally coherent Grothendieck category
whose derived category is compactly generated. As a source of such categories, we …

In a compactly generated triangulated category, we introduce a class of tilting objects
satisfying a certain purity condition. We call these the decent tilting objects and show that the …

arXiv:2310.01834v1 [math.RT] 3 Oct 2023 Page 1 arXiv:2310.01834v1 [math.RT] 3 Oct 2023
MUTATIONS AND DERIVED EQUIVALENCES FOR COMMUTATIVE NOETHERIAN RINGS …

We show that the cotilting heart associated to a tilting complex $ T $ is a locally coherent and
locally coperfect Grothendieck category (ie\a completion of an artinian abelian category) if …

Approximation theory is a fundamental tool in order to study the representation theory of a
ring R. Roughly speaking, it consists in determining suitable additive or abelian …

This thesis exhibits a class of t-structures, the intermediate restrictable ones, in the derived
category of a commutative noetherian ring R, whose hearts are derived and coderived …

We gently introduce the concept of abelian categories, motivated by the example of the
category of abelian groups, and we show that they provide all the ingredients needed for …