On relative derived categories

Asadollahi, Javad; Bahiraei, Payam; Hafezi, Rasool; Vahed, Razieh

doi:10.48550/arxiv.1311.2189

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2019

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“…The Gorenstein derived category was studied by Gao and Zhang [GZ]. Recently this category has been studied more in [ABHV,AHV1].…”

Section: 23mentioning

confidence: 99%

Derived equivalences of functor categories

Asadollahi

Hafezi

Vahed

2019

Journal of Pure and Applied Algebra

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Let Mod-S denote the category of S-modules, where S is a small category. In the first part of this paper, we provide a version of Rickard's theorem on derived equivalence of rings for Mod-S. This will have several interesting applications. In the second part, we apply our techniques to get some interesting recollements of derived categories in different levels. We specialize our results to path rings as well as graded rings.The differential∂ n is the induced map on residue classes.We denote the homotopy category of C by K(C); the objects are complexes and morphisms are the homotopy classes of morphisms of complexes. The full subcategory of K(C) consisting of all bounded above, resp. bounded, complexes is denoted by K − (C), resp. K b (C). Moreover, we denote by K −,b (C), the full subcategory of K − (A) formed by all complexes X such that there is an integer n = n(X) with H i (X) = 0, for all i ≤ n.

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“…The Gorenstein derived category was studied by Gao and Zhang [GZ]. Recently this category has been studied more in [ABHV,AHV1].…”

Section: 23mentioning

confidence: 99%