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

TL;DR

This paper demonstrates that on a ringed space with a soft structure sheaf, the dg-category of twisted perfect complexes is quasi-equivalent to the dg-category of vector bundle complexes, extending classical soft sheaf results.

Contribution

It establishes a dg-enhancement of the classical soft sheaf result by proving the quasi-equivalence of these dg-categories.

Findings

The dg-category of twisted perfect complexes is quasi-equivalent to vector bundle complexes.

This extends the classical soft sheaf results in SGA6.

Provides a dg-analogue of known soft sheaf properties.

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.