Related papers: Almost $\cal D$-split sequences and derived equiva…
We introduce a relative tilting theory in abelian categories and show that this work offers a unified framework of different previous notions of tilting, ranging from Auslander-Solberg relative tilting modules on Artin algebras to…
Given the pair of a dualizing $k$-variety and its functorially finite subcategory, we show that there exists a recollement consisting of their functor categories of finitely presented objects. We provide several applications for Auslander's…
In this paper, we study the sequences with (non-consecutive) two zero-symbols and ideal autocorrelation, which are also known as almost $m$-ary nearly perfect sequences. We show that these sequences are equivalent to $\ell$-partial direct…
In this paper, we will consider a class of locally $\Phi$-Beilinson-Green algebras, where $\Phi$ is an infinite admissible set of the integers, and show that symmetric approximation sequences in $n$-exangulated categories give rise to…
We construct an isomorphism between the partially ordered set of tilting modules for the Auslander algebra of $K[x]/(x^n)$ and the interval of rational permutation braids in the braid group on $n$ strands. Hence, there are only finitely…
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…
We provide a complete classification of all tilting modules and tilting classes over almost perfect domains, which generalizes the classifications of tilting modules and tilting classes over Dedekind and 1-Gorenstein domains. Assuming the…
We introduce the notion of AIR tilting subcategories of extended hearts of $t$-structures on a triangulated category associated with silting subcategories. This notion generalizes $\tau_{[d]}$-tilting pairs of extended finitely generated…
New exact modular branching rules are obtained for modules over the symmetric groups that are close to completely splittable modules. These results are based on some upper bounds for the Ext^1-spaces between simple modules.
We study twisted derived equivalences for schemes in the setting of spectral algebraic geometry. To this end, we introduce the notion of a twisted equivalence and show that a twisted equivalence for perfect spectral algebraic stacks…
Given a certain kind of linear representation of a reductive group, referred to as a quasi-symmetric representation in recent work of \v{S}penko and Van den Bergh, we construct equivalences between the derived categories of coherent sheaves…
We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizations of this kind and yields a way to obtain more tilted…
We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices of differential forms. The differential forms are elements of the middle dimensional cohomology whose variation is described by a variation of mixed…
Auslander-Reiten theory is fundamental to study categories which appear in representation theory, for example, modules over artin algebras, Cohen-Macaulay modules over Cohen-Macaulay rings, lattices over orders, and coherent sheaves on…
We introduce the concept of an $n$-minimal Auslander--Gorenstein category and $n$-precluster tilting subcategory. With this, we create an analog of the higher Auslander--Solberg correspondence (arXiv:1608.04179) for exact categories. Our…
We classify spherical modules and full exceptional sequences of modules over the Auslander algebra of $k[x]/(x^t)$. We categorify the left and right symmetric group actions on these exceptional sequences to two braid group actions: of…
Let $\Lambda$ be an artin algebra and $S(\Lambda)$ the category of all embeddings $(A\subseteq B)$ where $B$ is a finitely generated $\Lambda$-module and $A$ is a submodule of $B$. Then $S(\Lambda)$ is an exact Krull-Schmidt category which…
In extended hearts of bounded $t$-structures on a triangulated category, we provide a Happel-Reiten-Smalo tilting theorem and a characterization for $s$-torsion pairs. Applying these to $m$-extended module categories, we characterize…
In this paper, we introduce and study relative Auslander--Gorenstein pairs. This consists of a finite-dimensional Gorenstein algebra together with a self-orthogonal module that provides a further homological feature of the algebra in terms…
The paper is devoted to study some of the questions arises naturally in connection to the notion of relative derived categories. In particular, we study invariants of recollements involving relative derived categories, generalise two…