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Homology of FI-modules

Thomas Church and Jordan S Ellenberg

Geometry & Topology 21 (2017) 2373–2418

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.

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FI-modules, homology, Castelnuovo-Mumford regularity
Mathematical Subject Classification 2010
Primary: 18G10, 20C30
Received: 22 February 2016
Revised: 31 August 2016
Accepted: 3 September 2016
Published: 19 May 2017
Proposed: Benson Farb
Seconded: Haynes Miller, Jesper Grodal
Thomas Church
Department of Mathematics
Stanford University
450 Serra Mall
Stanford, CA 94305
United States
Jordan S Ellenberg
Department of Mathematics
University of Wisconsin
480 Lincoln Drive
Madison, WI 53706
United States