Geometry & Topology
- Geom. Topol.
- Volume 21, Number 4 (2017), 2373-2418.
Homology of FI-modules
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.
Geom. Topol., Volume 21, Number 4 (2017), 2373-2418.
Received: 22 February 2016
Revised: 31 August 2016
Accepted: 3 September 2016
First available in Project Euclid: 19 October 2017
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Church, Thomas; Ellenberg, Jordan. Homology of FI-modules. Geom. Topol. 21 (2017), no. 4, 2373--2418. doi:10.2140/gt.2017.21.2373. https://projecteuclid.org/euclid.gt/1508437644