2015/06/30 by Thomas M. Church, Thomas Church, Jordan S. Ellenberg
Computer Science · Mathematics · #Combinatorics #Commutative Algebra and Its Applications #Discrete mathematics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Pure mathematics #Topological and Geometric Data Analysis #Upper and lower bounds #math.AT #math.CO #math.GT #math.RT
paper · pdf · doi:10.2140/gt.2017.21.2373
published as Geom. Topol. 21 (2017) 2373-2418 · 34 pages. v2: major reorganization; to appear in Geometry and Topology
arxiv created 2016/09/05 · openalex publication_date 2017/05/19 · arxiv updated 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove an explicit and sharp upper bound for the Castelnuovo–Mumford regularity of an FI-module in terms of the degrees of its generators and relations. We use this to refine a result of Putman on the stability of homology of congruence subgroups, extending his theorem to previously excluded small characteristics and to integral homology while maintaining explicit bounds for the stable range. ¶ An equivalent version of this paper can be found on arXiv.