Geometry & Topology

Homology of FI-modules

Thomas Church and Jordan Ellenberg

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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.

Article information

Source
Geom. Topol., Volume 21, Number 4 (2017), 2373-2418.

Dates
Received: 22 February 2016
Revised: 31 August 2016
Accepted: 3 September 2016
First available in Project Euclid: 19 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1508437644

Digital Object Identifier
doi:10.2140/gt.2017.21.2373

Mathematical Reviews number (MathSciNet)
MR3654111

Zentralblatt MATH identifier
1371.18012

Subjects
Primary: 18G10: Resolutions; derived functors [See also 13D02, 16E05, 18E25] 20C30: Representations of finite symmetric groups

Keywords
FI-modules homology Castelnuovo-Mumford regularity

Citation

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


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