Homology of FI-modules

Church, Thomas; Ellenberg, Jordan

doi:10.2140/gt.2017.21.2373

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Homology of FI-modules

Thomas Church and Jordan S Ellenberg

Geometry & Topology 21 (2017) 2373–2418

DOI: 10.2140/gt.2017.21.2373

Abstract

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.

Keywords

FI-modules, homology, Castelnuovo-Mumford regularity

Mathematical Subject Classification 2010

Primary: 18G10, 20C30

References

Publication

Received: 22 February 2016

Revised: 31 August 2016

Accepted: 3 September 2016

Published: 19 May 2017

Proposed: Benson Farb

Seconded: Haynes Miller, Jesper Grodal

Authors

Thomas Church
Department of Mathematics Stanford University 450 Serra Mall Stanford, CA 94305 United States
http://math.stanford.edu/~church/
Jordan S Ellenberg
Department of Mathematics University of Wisconsin 480 Lincoln Drive Madison, WI 53706 United States
http://www.math.wisc.edu/~ellenber/

Volume 21, issue 4 (2017)