The descent of twisted perfect complexes on a space with soft structure   sheaf
  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. 
Zhaoting Wei
math.AG math.CT math.KT