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Nodal quintic del Pezzo threefolds and their derived categories
We construct a Kawamata type semiorthogondal decomposition for the bounded derived category of coherent sheaves of nodal quintic del Pezzo...
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Classifying Recollements of Derived Module Categories for Derived Discrete Algebras
We study a class of derived discrete Nakayama algebras. All indecomposable compact objects in the derived module category are determined and all...
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The Relation Between Gorenstein Derived and Pure Derived Categories
In this paper we study the relation between Gorenstein derived and pure derived categories under some conditions. Then, we also study the relation...
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On equivariant derived categories
We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. In...
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Recollements of Derived Categories from Two-Term Big Tilting Complexes
We introduce the notion of big tilting complexes over associative rings, which is a simultaneous generalization of good tilting modules and tilting...
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Triangulated categories of periodic complexes and orbit categories
We investigate the triangulated hull of orbit categories of the perfect derived category and the bounded derived category of a ring concerning the...
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Derived categories of skew quadric hypersurfaces
The existence of a full strong exceptional sequence in the derived category of a smooth quadric hypersurface was proved by Kapranov. In this paper,...
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Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra
We mostly review work of Taelman (Derived equivalences of hyperkähler varieties, 2019, ar**v:1906.08081 ) on derived categories of hyper-Kähler...
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Indecomposability of derived categories for arbitrary schemes
We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For...
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The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two...
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Derived categories of NDG categories
In this paper we study N-differential graded categories and their derived categories. First, we introduce modules over an N-differential graded...
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Compactly generated tensor t-structures on the derived categories of Noetherian schemes
We introduce a tensor compatibility condition for t-structures. For any Noetherian scheme X , we prove that there is a one-to-one correspondence...
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Lifting (co)stratifications between tensor triangulated categories
We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact R -linear...
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Serre Functors and Graded Categories
We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k -lin...
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An equivalence of categories
We prove a result of Block, that gives an equivalence of categories between the homotopy category of antiholomorphic superconnections on X and the...
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Faltings’ annihilator theorem and t-structures of derived categories
In this paper, we prove Faltings’ annihilator theorem for complexes over a CM-excellent ring. As an application, we give a complete classification of...
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Hochschild (Co)homology and Derived Categories
These are slightly expanded notes of lectures given in April 2019 at the Isfahan school and conference on representations of algebras. We recall the...
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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...