We generalize Brenner and Butler’s Theorem as well as Happel’s Theorem on the equivalences induced by a finitely generated tilting module over Artin algebras, to the case of an infinitely generated tilting module over an arbitrary associative ring establishing the equivalences induced between subcategories of module categories and also at the level of derived categories.

In this paper, we will consider a class of locally $\Phi$-Beilinson-Green algebras, where $\Phi$ is an infinite admissible set the integers, and show that symmetric approximation sequences in $n$-exangulated categories give rise to derived equivalences between quotient algebras principal diagonals modulo some factorizable ghost coghost ideals by finite tilting family. Then get equivalent have n...

Image formation is described by means of modern geometry in terms of topological and geometric curvatures. These curvatures and derived equivalences are a quantisation of the set of rules for constructing the image in particular along discontinuity, singularity and bifurcation sets. A simpliication of the set of construction rules is proposed by applying a dynamic scale-space paradigm. Dynamic ...

We show that the derived equivalence between full defect blocks of S L ( 2 , q ) in defining characteristic and their Brauer correspondants can be presented as a composition perverse equivalences.

Over a commutative noetherian ring $R$, the prime spectrum controls, via assignment of support, structure both $\mathsf{Mod}(R)$ and $\mathsf{D}(R)$. We show that, just like in $\mathsf{Mod}(R)$, support classifies hereditary torsion pairs heart any nondegenerate compactly generated $t$-structure Moreover, we investigate whether these $t$-structures induce derived equivalences, obtaining new so...