Homology of FI-modules
Representation Theory
2017-06-14 v2 Algebraic Topology
Combinatorics
Geometric Topology
Abstract
We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V 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.
Cite
@article{arxiv.1506.01022,
title = {Homology of FI-modules},
author = {Thomas Church and Jordan S. Ellenberg},
journal= {arXiv preprint arXiv:1506.01022},
year = {2017}
}
Comments
34 pages. v2: major reorganization; to appear in Geometry and Topology