… This theory goes back to Auslander's notion of modules of G-dimension zero [4]. Later it was
… aim to study singularity categories through silting theory. Recall that silting theory was first …

… non-zero silting object belongs to the singularity category Dsg(… of Λ is finite, then the singularity
category is zero. If Λ is (non-… category is triangle equivalent to the singularity category [5]. …

… relation between silting subcategories and tilting subcategories in extriangulated categories,
… the description of the singularity category due to Happel and Chen-Zhang by this reduction. …

… version of the description of the singularity category due to Happel and Chen-Zhang. …
In Section 2, we recall the definition of silting subcategory in exact category and some basic …

… categories, we show that the heart of a (co)silting t-structure is a Grothendieck category if and
only if the (co)silting object … If we further assume our triangulated category to be algebraic, it …

… The main goal of this paper is to compare the silting theory of … obtain an isomorphism between
the silting poset of A and that … of recent developments in silting theory by Angeleri Hügel. …

… of silting and tilting objects in triangulated categories. Tilting objects play an important role in
the Morita theory of derived categories and silting … on the bounded derived category of finite-…

… basic results for silting theory ans simple-minded collections. In Section 3, we investigate
the localization of the bounded derived category of a hereditary abelian category with respect …

… In particular, we study relative derived categories and silting complexes over abelian categories.
Let \({\mathcal {A}} \) be an abelian category with coproducts, \({\mathcal {S}} \subseteq {…

… silting objects, and such a triangulated category has so nice structure. For example, a
silting-discrete triangulated category … categories without silting: • the singularity category Dsg(Λ) for …