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

2015/04/30 by Zhaoting Wei
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Construct (python library) #Field (mathematics) #Homotopy and Cohomology in Algebraic Topology #Space (punctuation) #Topological and Geometric Data Analysis #Topology (electrical circuits) #math.AG #msc:14F05 #msc:16E45 #msc:18E30

paper · pdf · doi:10.1007/s40879-016-0102-8

published as European Journal of Mathematics, 2 (2016), No. 3, 716-759 · 33 pages, multiple changes from the second version

arxiv created 2016/03/11 · openalex publication_date 2016/03/16 · openalex created_date 2016/06/24 · arxiv updated 2016/12/26 · openalex updated_date 2026/08/05

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.

Citations