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19
Stratifying triangulated categories
, 2009
"... A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences which follow when T is stratified by R. Among them are a cl ..."
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Cited by 17 (5 self)
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A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences which follow when T is stratified by R. Among them are a classification of the localizing subcategories of T in terms of subsets of the set of prime ideals in R; a classification of the thick subcategories of the subcategory of compact objects in T; and results concerning the support of the Rmodule of homomorphisms Hom ∗ T (C, D) leading to an analogue of the tensor
HOCHSCHILD DIMENSION OF TILTING OBJECTS
, 2009
"... We give a new upper bound for the generation time of a tilting object and use it to verify, in some new cases, a conjecture of Orlov on the dimension of the derived category of coherent sheaves on a smooth variety. ..."
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Cited by 5 (3 self)
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We give a new upper bound for the generation time of a tilting object and use it to verify, in some new cases, a conjecture of Orlov on the dimension of the derived category of coherent sheaves on a smooth variety.
ExtSYMMETRY OVER QUANTUM COMPLETE INTERSECTIONS
, 811
"... Abstract. We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric. 1. ..."
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Cited by 4 (2 self)
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Abstract. We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric. 1.
nrepresentation infinite algebras
"... From the viewpoint of higher dimensional AuslanderReiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call nrepresentation infinite. They are a certain analog of representation infinite hereditary algebras, and we study three important classes o ..."
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Cited by 4 (0 self)
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From the viewpoint of higher dimensional AuslanderReiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call nrepresentation infinite. They are a certain analog of representation infinite hereditary algebras, and we study three important classes of modules: npreprojective, npreinjective and nregular modules. We observe that their homological behaviour is quite interesting. For instance they provide first examples of algebras having infinite Ext 1orthogonal families of modules. Moreover we give general constructions of nrepresentation infinite algebras. Applying Minamoto’s theory on Fano algebras in noncommutative algebraic geometry, we describe the category of nregular modules in terms of the corresponding preprojective algebra. Then we introduce nrepresentation tame algebras, and show that the category of nregular modules decomposes into the categories of finite dimensional modules over localizations of the preprojective algebra. This generalizes the classical description of regular modules over tame hereditary algebras. As an application, we show that the representation dimension of an nrepresentation tame algebra is at least n+2.
THE DIMENSION OF THE DERIVED CATEGORY OF ELLIPTIC CURVES AND TUBULAR WEIGHTED PROJECTIVE
"... Abstract. We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal. 1. ..."
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Abstract. We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal. 1.
COHOMOLOGICAL SYMMETRY IN TRIANGULATED CATEGORIES
"... Abstract. We give a criterion for cohomological symmetry in a triangulated ..."
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Abstract. We give a criterion for cohomological symmetry in a triangulated
On the vanishing of cohomology in triangulated categories
, 2008
"... We study the vanishing of cohomology in a triangulated category, in particular vanishing gaps and symmetry. ..."
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Cited by 2 (1 self)
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We study the vanishing of cohomology in a triangulated category, in particular vanishing gaps and symmetry.
Annihilation of cohomology and strong generators for module categories, available at arXiv:1404.1476
"... ar ..."