A long exact sequence for homology of FI-modules

Wee Liang Gan

A long exact sequence for homology of FI-modules

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arxiv 1602.08873 v3 pith:PVNCLCWK submitted 2016-02-29 math.RT

Wee Liang Gan This is my paper · ORCID

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keywords degreeexactfi-modulehomologylongsequencefinitegenerated

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We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo-Mumford regularity of an FI-module which is generated and related in finite degree. We also prove that for an FI-module which is generated and related in finite degree, if it has a nonzero higher homology, then its homological degrees are strictly increasing (starting from the first homological degree).

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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.

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