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Recollements induced by good (co)silting dg-modules
Let U be a dg- A -module, B the endomorphism dg-algebra of U . We know that if U is a good silting object, then there exist a dg-algebra C and a...
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Silting Reduction in Exact Categories
Presilting and silting subcategories in extriangulated categories were introduced by Adachi and Tsukamoto recently, which are generalizations of...
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A geometric realization of silting theory for gentle algebras
A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into polygons and the bounded derived category of the gentle...
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Derived Equivalences Induced by Good Silting Complexes
We study the equivalences induced by some special silting objects in the derived category over dg-algebra whose positive cohomologies are all zero.
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Gorenstein Weak n-Silting Modules and Weak n-Star Modules
As generalizations of silting modules and star modules, respectively, the notions and basic properties of Gorenstein weak n -silting and weak n -star...
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A Relative Silting Theorem
Silting theorem gives a generalization of the classical tilting theorem of Brenner and Butler for a 2-term silting complex. In this paper, we give a...
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A generalization of silting modules and Tor-tilting modules
We introduce the concept of weak silting modules, which is a generalization of both silting modules and Tor-tilting modules. It is shown that W is a...
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Partial silting objects and smashing subcategories
We study smashing subcategories of a triangulated category with coproducts via silting theory. Our main result states that for derived categories of...
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Two terms tilting complexes and Ringel–Hall algebras
In this paper, we show that under certain mild assumptions, each 2-term silting complex induces isomorphisms between certain subalgebras of...
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A Bongartz-type lemma for silting complexes over a hereditary algebra
Let A be a finite dimensional algebra, the Bongartz lemma for classic tilting modules says that any partial tilting module is a direct summand of a...
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A complete derived invariant for gentle algebras via winding numbers and Arf invariants
Gentle algebras are in bijection with admissible dissections of marked oriented surfaces. In this paper, we further study the properties of...
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From classical tilting to two-term silting
We survey some recent results generalizing classical tilting theory to a theory of two-term silting objects. In particular, this includes a...
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Gluing compactly generated t-structures over stalks of affine schemes
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...
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Injective Cogenerators, Cotilting Modules and Cosilting Modules
It is well known that the concept of cotilting modules generalizes injective cogenerators and in turn, the concept of cosilting modules generalizes...
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The Structure of Aisles and Co-aisles of t-Structures and Co-t-structures
Right triangulated categories can be thought of as triangulated categories whose shift functor is not an equivalence. We give intrinsic...
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Exceptional sequences in the derived category of a gentle algebra
In this paper, using the correspondence of gentle algebras and dissections of marked surfaces, we study full exceptional sequences in the perfect...
