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 study the transfer of (co) silting objects in derived categories of module categories via
the extension functors induced by a morphism of commutative rings. It is proved that the …

We investigate parametrizations of compactly generated t-structures, or more generally, t-
structures with a definable coaisle, in the unbounded derived category $\mathrm …

Over a commutative noetherian ring R, the prime spectrum controls, via the assignment of
support, the structure of both Mod (R) and D (R). We show that, just like in Mod (R), the …

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 …

We show that compactly generated t-structures in the derived category of a commutative ring
R are in a bijection with certain families of compactly generated t-structures over the local …

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 …

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 …