2012/10/31 by Thomas M. Church, Thomas Church, Jordan S. Ellenberg +2 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Diagonal #Discrete mathematics #Geometry #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Noetherian #Pure mathematics #math.AT #math.CO #math.GT #math.RT
paper · pdf · doi:10.2140/gt.2014.18.2951
published as Geom. Topol. 18 (2014) 2951-2984 · 32 pages; v2: reorganized paper, expanded introduction and added Theorems B and C
arxiv created 2014/03/02 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
FI-modules were introduced by the first three authors to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S n -representations. In this paper we prove the Noetherian property for FI-modules over arbitrary Noetherian rings: any sub-FI-module of a finitely generated FI-module is finitely generated. This lets us extend many results to representations in positive characteristic, and even to integral coefficients. We focus on three major applications of the main theorem: on the integral and mod p cohomology of configuration spaces; on diagonal coinvariant algebras in positive characteristic; and on an integral version of Putman's central stability for homology of congruence subgroups.