2013/03/20 by Brahim Benzeghli, Benzeghli, Brahim · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CT
paper · pdf · doi:10.48550/arxiv.1303.4941
arxiv created 2013/03/20 · openalex publication_date 2013/03/20 · arxiv updated 2013/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pridham has shown that any Artin n-stack M has a presentation as a simplicial scheme X satisfying certain smoothness properties originally introduced by Grothendieck. In the previous paper we introduced an Artin n-stack M of Maurer-Cartan elements of a dg-category and constructed a chart, and have already proven the first conditions of smoothness of X1→ X0 explicitly. In this paper, we will construct explicitly the full simplicial scheme and show the Grothendieck-Pridham smoothness conditions, implying that M is a geometric n-stack.