Thick subcategory
Web19 Dec 2013 · We show that every thick subcategory of the singularity category of a complete intersection ring is self dual. We also prove the analogous statement for thick subcategories of the bounded derived category and give applications to the symmetry of vanishing of cohomology. In order to prove these results for the bounded derived … WebLocalization Biresolving subcategory Biresolving subcategory Let (C;E;s) be an extriangulated category. De nition Let N be an additive subcategory of C. N is a thick subcategory if it satis es the two out of three property with respect to any s-con ation. Moreover N is called a biresolving subcategory if it satis es the following condition.
Thick subcategory
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WebFor a triangulated category with a bounded t-structure, we prove that there is a bijection between wide subcategories of its heart and thick subcategories of the triangulated … Web1 Jan 1997 · The first main result of this paper is a bijective correspondence between the strictly full triangulated subcategories dense in a given triangulated category and the …
WebWe show that every thick subcategory of the singularity category of a complete intersection ring is self dual. We also prove the analogous statement for thick subcategories of the bounded derived category and give applications to the symmetry of vanishing of cohomology. In order to prove these results for the bounded derived category, we extend … Webobjects, which is useful in studying its thick subcategories, for example. The work presented here arose from a search for a more direct proof of this result. Our reason 2010 Mathematics Subject Classi cation. 18E30 (primary), 13D45, 16E35, 20J06. Key words and phrases. cohomological functor, local cohomology, local-global principle, support.
WebSince a thick subcategory is a triangulated category, its dimension in the sense of Rouquier can be defined. It turned out, by work of Oppermann and Sˇ´tov ´ıcek [ˇ 26], that over a noetherian algebra (respectively, a projective scheme) all proper thick subcategories of the bounded derived category of finitely WebTo do this we introduce certain generating sets called ES-collections which correspond to configurations of non-crossing arcs on a geometric model. We show that every thick …
Web1 Jul 2007 · Under this isomorphism, a thick support S corresponds to the thick subcategory T S consisting of all complexes X such that Supp (X) ⊆ S, and a thick subcategory C corresponds to the thick support ⋃ X ∈ C Supp (X). Using this theorem, we now work our way to the Krull–Schmidt theorem for thick subcategories of perfect …
Web14 Jun 2024 · My question is whether this subcategory is thick. triangulated-categories; Share. Cite. Follow asked Jun 14, 2024 at 3:10. user12580 user12580. 837 5 5 silver … steven mounce louisianaWebsification of the thick subcategories of perfect Differential Graded modules over suitableDGalgebras. TheresultaboutkG-modulesisthendeducedfromitbya series of reductions, following the paradigm developed in the work of the second ... full subcategory consisting of DG modules M for which the S-module H(M)is finitely generated. The basic ... steven motors wichitaWebA subcategory of a triangulated category is said to be thick, or ´epaisse, if it is a triangulated subcategory and it is closed under taking direct summands. One product of the deep work … steven mukuka v the peopleA nonempty full subcategory TT of an abelian category AA is thick(in the strong sense) if for every exact sequence in AA, the object M″M'' is in TT iff MM and M′M' are in TT. In words, it is an additive full subcategory closed under subobjects, quotients and extensions (e.g. Dichev 2009 and Pierre Gabriel in Des … See more A non-empty full (pre-)triangulated subcategory is called thick (or épaisse) if it is “closed under direct summands” (e.g. Murayama, Def. 11, see Stacks Project, Def. 13.6.1). See more Recall that a class Σ\Sigma of morphisms with category of fractions 𝒞Σ\mathcal{C}_\Sigma is called saturated if Σ\Sigma coincides with the class of morphisms inverted … See more Following the extensions of an early work of Serre by Grothendieck and Gabriel, for any thick subcategory TT in an abelian category AA, one defines the (Serre) quotient category … See more steven mounsey penrithWebGiven an arbitrary triangulated category T, a thick subcategory Sis a full subcategory of Twhich is closed under nite direct sums and summands. We will call a subcategory SˆT localizing if it is thick and closed under small coproducts. Similarly, we will call a subcategory colocalizing if it is thick and closed under small products. De nition 2. steven mullins north ridgeville ohioWeb5 Jun 2024 · A thick subcategory $ \mathfrak A ^ \prime $ is a localizing subcategory if and only if: 1) every object of $ \mathfrak A $ has a largest subobject in $ \mathfrak A ^ … steven murdoch allan southwarkWebthick subcategory is generated by an ES-collection (Theorem4.9). There are two properties of exceptional collections which make them particularly nice to deal with, as generators of … steven motors inc wichita ks