The descent of twisted perfect complexes on a space with soft structure sheaf

Abstract

In this paper we study the dg-category of twisted perfect complexes on a ringed space with soft structure sheaf. We prove that this dg-category is quasi-equivalent to the dg-category of complexes of vector bundles on that space. This result could be considered as a dg-enhancement of the classic result on soft sheaves in SGA6.

20 pages. v2: minor changes. Note that part of this paper, in particular Section 3.2, has been integrated in to arXiv:1804.00993, although the notations and viewpoint are slightly different. v3: minor changes, reference updated