Thick subcategory
WebLet T be a triangulated category. A subcategory A is called thick or épaisse if it is closed under isomorphisms and direct summands. Definition 6. Let T be a triangulated category. A subcategory A is called dense if every object of T is isomorphic to … WebA full subcategory C of Mod A is called thick if for each exact sequence M1 → M2 → M3 → M4 → M5 of A-modules with Mi in C for i = 1,2,4,5, the module M3 belongs to C. It is clear …
Thick subcategory
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Webof T is a thick subcategory, which implies that SppX = Spp(thickX) for each full subcategory X of T . Proof. This is a direct consequence of the definition of a thick subcategory. Indeed, the fact that a thick subcategory contains the zero object shows (1), the fact that it is closed under shifts shows (2), the fact WebIt seems to me that a classification of thick subcategories of a (tensor-) triangulated category is a good thing to have when you have some, relatively generic, thick …
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 … http://eprints.gla.ac.uk/143894/
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 … 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 …
WebHiroki Matsui. Vol. 313 (2024), No. 2, 433–457. DOI: 10.2140/pjm.2024.313.433. Abstract. For an essentially small triangulated category T, we introduce the notion of prime thick …
Web2 Aug 1994 · subcategory is dense in a uniquely determined thick triangulated subcategory, this result refines any known classification of thick subcategories to a classification of … my child talks in his sleepWeb13 Jun 2024 · 1. Introduction. The singularity category of a commutative Noetherian ring A is the Verdier quotient of the finite bounded derived category of A by the subcategory of … my child swearsWebCitation Download Citation. Ryo TAKAHASHI. "Thick subcategories over Gorenstein local rings that are locally hypersurfaces on the punctured spectra." office depot $ 40 off couponWebThe thick subcategories of finite spectra and those of perfect com-plexes in the derived category of a Noetherian ring admit Krull-Schmidt decompo-sitions. Conversely, in both … my child talks to himselfWeb21 Oct 2024 · P 2 Th(T) is a prime thick subcategory if P has a unique cover in Th(T). Spec (T) := fprime thick subategories of T g We will see later that for a radical ideal P of Dpf(X), … office depot $5 mcafee offerWebA 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 … my child tax benefit accountWebA parallel notion is more relevant for "small" triangulated categories: a thick subcategory of a triangulated category C is a strictly full triangulated subcategory that is closed under … my child talks too loud