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Homology of FI-modules

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arxiv 1506.01022 v2 pith:GODWLJZV submitted 2015-06-02 math.RT math.ATmath.COmath.GT

Thomas Church , Jordan S. Ellenberg This is my paper · ORCID
classification math.RTmath.ATmath.COmath.GT
keywords homologyexplicitboundboundscastelnuovo-mumfordcharacteristicscongruencedegrees
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An inductive method for $\mathrm{OI}$-modules

    math.RT 2019-09 accept novelty 7.0 of 10

    An explicit double-exponential upper bound on the regularity of OI-modules presented in finite degrees, together with a new inductive method for proving their structural properties.

  2. Representation stability in the (co)homology of vertical configuration spaces

    math.AT 2024-12 accept novelty 6.0 of 10

    The (co)homology of vertical configuration spaces is representation stable as S_k≀S_n-representations, with explicit stable ranges and an improved homological stability range for the unordered spaces.

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