共查询到20条相似文献,搜索用时 0 毫秒
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This is the third paper in a series. In Part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and derived categories of abelian categories. Then we consider examples from (noncommutative) algebraic geometry. In particular, we study noncommutative Grassmanians that are true noncommutative moduli spaces of structure sheaves of projective subspaces in projective spaces. 相似文献
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Dongyuan Yao 《K-Theory》1996,10(3):307-322
Let A be an Abelian category and B be a thick subcategory of A. Let D
b(B) denote the derived category of cohomologically bounded chain complexes of objects in A and D
B
b
(A) denote the derived category of cohomologically bounded chain complexes of objects in A with cohomology in B. We give two if and only if conditions for equivalence of D(B) and D
B
b
(A), and we give an example where D
b
(B) and D
B
b
(A) are not equivalent. 相似文献
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George Ciprian Modoi 《代数通讯》2013,41(3):995-1011
We say that a projective class in a triangulated category with coproducts is perfect if the corresponding ideal is closed under coproducts of maps. We study perfect projective classes and the associated phantom and cellular towers. Given a perfect generating projective class, we show that every object is isomorphic to the homotopy colimit of a cellular tower associated to that object. Using this result and the Neeman's Freyd-style representability theorem, we give a new proof of Brown Representability Theorem. 相似文献
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XiaoJuan Zhao 《中国科学 数学(英文版)》2014,57(11):2329-2334
Let A and B be finite-dimensional algebras over a field k of finite global dimension. Using some results of Gorsky in “Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras”, we prove that if A and B are derived equivalent, then the corresponding m-periodic derived categories are triangulated equivalent. 相似文献
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In this article we provide arguments for constructing Kaplansky classes in the category of complexes out of a Kaplansky class of modules. This leads to several complete cotorsion theories in such categories. Our method gives a unified proof for most of the known cotorsion theories in the category of complexes and can be applied to the category of quasi-coherent sheaves over a scheme as well as the category of the representations of a quiver. 相似文献
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Let E be a proper class of triangles in a triangulated category C, and let (A, B, C) be a recollement of triangulated categories. Based on Beligiannis's work, we prove that A and C have enough E-projective objects whenever B does. Moreover, in this paper, we give the bounds for the E-global dimension of B in a recollement (A, B, C) by controlling the behavior of the E-global dimensions of the triangulated categories A and C: In particular, we show that the finiteness of the E-global dimensions of triangulated categories is invariant with respect to the recollements of triangulated categories. 相似文献
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OGUISO Keiji 《中国科学 数学(英文版)》2011,(8)
A non-representable cohomological functor of finite type of the bounded derived category of coherent sheaves of a compact complex manifold of dimension greater than one with no proper closed subvariety is given explicitly in categorical terms.This is a partial generalization of an impressive result due to Bondal and Van den Bergh. 相似文献
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For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are characterized and two consequences for the class of hereditary rings are established: homological epimorphisms and universal localizations coincide, and the telescope conjecture for the derived category holds true. However, we present examples showing that neither of these two statements is true in general for rings of global dimension 2. 相似文献
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This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Defh(E), coDefh(E), Def(E), coDef(E). The first two functors describe the deformations (and co-deformations) of E in the homotopy category, and the last two - in the derived category. We study their properties and relations. These functors are defined on the category of artinian (not necessarily commutative) DG algebras. 相似文献
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This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation functors to an appropriate bicategory of artinian DG algebras and prove that these extended functors are pro-representable in a strong sense. 相似文献
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We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5Z-quotient of the Fermat quintic surface in P3. This is the maximal possible length of such a sequence on this surface which has Grothendieck group Z11⊕Z/5Z. In particular, the result answers Kuznetsov’s Nonvanishing Conjecture, which concerns Hochschild homology of an admissible subcategory, in the negative. The sequence carries a symmetry when interpreted in terms of the root lattice of the simple Lie algebra of type E8. We also produce explicit nonzero objects in the (right) orthogonal to the exceptional sequence. 相似文献
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Mustafa Kemal Berktaş Septimiu Crivei Fatma Kaynarca Derya Keskin Tütüncü 《Journal of Pure and Applied Algebra》2021,225(6):106621
Two uniqueness theorems on uniform decompositions due to Krause, Diracca and Facchini are extended from abelian categories to weakly idempotent complete exact categories. We give applications to (quasi-)abelian categories, finitely accessible additive categories and exactly definable additive categories. 相似文献
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Apostolos Beligiannis 《Algebras and Representation Theory》2002,5(5):483-525
Our aim in this paper is to develop a theory of purity and to prove in a unified conceptual way the existence of almost split morphisms, almost split sequences and almost split triangles in abstract homotopy categories, a rather omnipresent class of categories of interest in representation theory. Our main tool for doing this is the classical Brown representability theorem. 相似文献
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Global dimension and left derived functors of Hom 总被引:1,自引:0,他引:1
It is well known that the right global dimension of a ring R is usually computed by the right derived functors of Hom and the left projective resolutions of right R-modules. In this paper, for a left coherent and right perfect ring R, we characterize the right global dimension of R, from another point of view, using the left derived functors of Hom and the right projective resolutions of right R-modules. It is shown that rD(R)≤n (n≥2) if and only if the gl right Proj-dim MR≤n - 2 if and only if Extn-1(N, M) = 0 for all right R-modules N and M if and only if every (n - 2)th Proj-cosyzygy of a right R-module has a projective envelope with the unique mapping property. It is also proved that rD(R)≤n (n≥1) if and only if every (n-1)th Proj-cosyzygy of a right R-module has an epic projective envelope if and only if every nth Vroj-cosyzygy of a right R-module is projective. As corollaries, the right hereditary rings and the rings R with rD(R)≤2 are characterized. 相似文献
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We prove that the pure global dimension of a polynomial ring over an integral domain k in a finite or countable number n?2 of commuting (non-commuting, resp.) variables is t + 1, provided . As an application, we determine the pure global dimension of wild algebras of quiver type, also (in case k is an algebraically closed field) of the wild local and wild commutative algebras of finite k-dimension. 相似文献