Related papers: Silting objects

This paper focuses on recollements and silting theory in triangulated categories. It consists of two main parts. In the first part a criterion for a recollement of triangulated subcategories to lift to a torsion torsion-free triple (TTF…

First, we give a new example of silting-discrete algebras. Second, one explores when the algebra of triangular matrices over a finite dimensional algebra is $\tau$-tilting finite. In particular, we classify algebras over which triangular…

This paper is devoted to studying two important classes of objects in triangulated categories; silting objects and $d$-cluster tilting objects, and their correspondences. First, we introduce the notion of $d$-silting objects as a…

We develop silting theory of a noetherian algebra $\Lambda$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $\Lambda$, and as a consequence, we see that mutation exists. As in the case of…

We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of the silting subcategory. Moreover, we obtain its…

We introduce a discrete cobordism category for nested manifolds and nested cobordisms between them. A variation of stratified Morse theory applies in this case, and yields generators for a general nested cobordism category. Restricting to a…

We study silting objects over derived preprojective algebras of acyclic quivers by giving a direct relationship between silting objects, spherical twist functors and mutations. Especially, for a Dynkin quiver, we establish a bijection…

Let $R$ be a ring. In this paper, we study the characterization of cosilting modules and establish a relation between cosilting modules and cotilting objects in a Grothendieck category. We proved that each cosilting right $R$-module $T$ can…

Presilting and silting subcategories in extriangulated categories were introduced by Adachi and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization $\mathcal B/({\rm thick}\mathcal W)$ of an extriangulated…

We show that any (n+1)-term silting complex whose intermediate cohomology vanishes gives rise to an n-silting module, as recently introduced by Mao. Specializing to commutative noetherian rings, we show that this assignment induces a…

We study the equivalences induced by some special silting objects in the derived category over dg-algebra whose positive cohomologies are all zero.

In this work we introduce notions in Auslander-Buchweitz theory and cotorsion theory in extriangulated categories which extend the given ones for abelian categories. Although these notions have been already developed for extriangulated…

Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…

This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…

The focus of this article is on metric completions of triangulated categories arising in the representation theory of hereditary finite dimensional algebras and commutative rings. We explicitly describe all completions of bounded derived…

We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D(Mod-A) of a ring A. To this end, we provide a construction of t-structures…

We consider endomorphism algebras of $n$-term silting complexes in derived categories of hereditary algebras, and we show that the module category of such an endomorphism algebra has a separated $n$-section. For $n=3$ we obtain a trisection…

We give a reduction technique for silting intervals in extriangulated categories, which we call "silting interval reduction". It provides a reduction technique for tilting subcategories when the extriangulated categories are exact…

We introduce a notion of global dimension for a triangulated category relative to a compact silting object. We prove that the finiteness of this dimension is an intrinsic property of the triangulated category itself and, therefore,…

Extriangulated category was introduced by Nakaoka and Palu to give a unification of properties in exact categories and triangulated categories. A notion of tilting (or cotilting) subcategories in an extriangulated category is defined in…