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arXiv · 1504.05055

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

Zhaoting Wei
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Abstract

In this paper we study twisted complexes on a ringed space and prove that it gives a new dg-enhancement of the derived category of perfect complexes on that space. A twisted complex is a collection of locally defined sheaves together with the homotopic gluing data. In this paper we construct a dg-functor from twisted complexes to perfect complexes, which turns out to be a dg-enhancement. This new enhancement has the advantage of being completely geometric and it comes directly from the definition of perfect complex . In addition we will talk about some applications and further topics around twisted complexes.

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Zhaoting Wei. 2015-04-20. Twisted complexes on a ringed space as a dg-enhancement of perfect complexes. https://doi.org/10.1007/s40879-016-0102-8

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