2014/07/22 by Carmelo Di Natale, Di Natale, Carmelo
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #math.AG #math.CT
paper · pdf · doi:10.48550/arxiv.1407.5900
54 pages, Section 2.4 significantly extended, minor corrections to the rest of the paper
openalex publication_date 2014/07/22 · arxiv created 2015/09/15 · arxiv updated 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of this paper we construct a model structure for the category of filtered cochain complexes of modules over some commutative ring R and explain how the classical Rees construction relates this to the usual projective model structure over cochain complexes. The second part of the paper is devoted to the study of derived moduli of sheaves: we give a new proof of the representability of the derived stack of perfect complexes over a proper scheme and then use the new model structure for filtered complexes to tackle moduli of filtered derived modules. As an application, we construct derived versions of Grassmannians and flag varieties.