Twisted complexes on a ringed space as a dg-enhancement of the derived category of perfect complexes

Wei, Zhaoting

doi:10.1007/s40879-016-0102-8

Cited by 10 publications

(28 citation statements)

References 17 publications

(54 reference statements)

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“…In [Wei19] the formula in this note is used to construct A ∞ -inverse of dg-natural transformations between twisted complexes. Moreover in an upcoming work [Wei], the formula in this note, together with the method in [Wei16], [Wei18], [BHW17], and [AØ18], can be used to obtain an injective dg-resolution of the equivariant derived category [BL94].…”

Section: Therefore Letmentioning

confidence: 99%

A recurrent formula of $A_{\infty}$-quasi inverses of dg-natural transformations between dg-lifts of derived functors

Wei¹

2019

Preprint

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A dg-natural transformation between dg-functors is called an objectwise homotopy equivalence if its induced morphism on each object admits a homotopy inverse. In general an objectwise homotopy equivalence does not have a dg-inverse but has an A ∞ quasi-inverse. In this note we give a recurrent formula of the A ∞ quasi-inverse. This result is useful in studying the compositions of dg-lifts of derived functors of schemes.

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Section: Therefore Letmentioning

confidence: 99%

A recurrent formula of $A_{\infty}$-quasi inverses of dg-natural transformations between dg-lifts of derived functors

Wei¹

2019

Preprint

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“…For more details on twisted complexes see [Wei16]. In this paper we want to find the relation between twisted complexes and Cpx(N • ) where N • is the Cech nerve of U.…”

Section: Letmentioning

confidence: 99%

Explicit homotopy limits of $\mathrm{dg}$-categories and twisted complexes

Block

Holstein

Wei

2017

Homology, Homotopy and Applications

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In this paper we study the homotopy limits of cosimplicial diagrams of dg-categories. We first give an explicit construction of the totalization of such a diagram and then show that the totalization agrees with the homotopy limit in the following two cases: (1) the complexes of sheaves of O-modules on theČech nerve of an open cover of a ringed space (X, O); (2) the complexes of sheaves on the simplicial nerve of a discrete group G acting on a space. The explicit models we obtain in this way are twisted complexes as well as their D-module and G-equivariant versions. As an application we show that there is a stack of twisted perfect complexes.

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“…On the other hand, Toledo and Tong [TT78] introduced twisted complexes in the 1970's as a way to obtain global resolutions of perfect complexes of sheaves on a complex manifold. In 2015 Wei proved in [Wei16] that the dg-category of twisted perfect complexes give a dg-enhancement of the derived category of perfect complexes.…”

Section: The Global Sections Functormentioning

confidence: 99%

“…We give a brief review of twisted perfect complexes in this subsection, for reference see [OTT81] Section 1 or [Wei16] Section 2.…”

Section: A Quick Review Of Twisted Perfect Complexesmentioning

confidence: 99%

“…We use the terminology "twisted perfect complex" to emphasize that each E • i is a strictly perfect complex. In [Wei16] Section 2.5 it has been shown that Tw perf (X, A, U i ) has a pre-triangulated structure hence HoTw perf (X, A, U i ) is a triangulated category. In more details we have the following definitions.…”

Section: A Quick Review Of Twisted Perfect Complexesmentioning

confidence: 99%

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