1996/09/17 by Carlos Simpson, Simpson, Carlos
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9609014
LaTeX
arxiv created 1996/09/17 · openalex publication_date 1996/09/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a generalization of Artin's definition of algebraic stack, which we call \em geometric n-stack. The main observation is that there is an inductive structure to the definition whereby the ingredients for the definition of geometric n-stack involve only n-1-stacks and so are already previously defined. We use this inductive structure to obtain some basic properties. We look at maps from a projective variety into certain such n-stacks, and obtain an interpretation of the Brill-Noether locus as the set of points of a geometric n-stack. At the end we explain how this provides a context for looking at de Rham theory for higher nonabelian cohomology, how one can define the Hodge filtration and so on.