2017/10/18 by Kevin Casto, Casto, Kevin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #math.GT
paper · pdf · doi:10.48550/arxiv.1710.06850
arxiv created 2017/10/18 · openalex publication_date 2017/10/18 · arxiv updated 2017/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue the study of a general class of spaces of 0-cycles on a manifold defined and begun by Farb-Wolfson-Wood. Using work of Gadish on linear subspace arrangements, we obtain representation stability for the cohomology of the ordered version of these spaces. We establish subexponential bounds on the growth of unstable cohomology, and the Grothendieck-Lefschetz trace formula then allows us to translate these topological stability phenomena to stabilization of statistics for spaces of 0-cycles over finite fields. In particular, we show that the average value of certain arithmetic quantities associated to rational maps over finite fields stabilizes as the degree goes to infinity.