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Depth and the Local Cohomology of FI_G-modules

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arxiv 1602.04405 v3 pith:YZOBS5IU submitted 2016-02-13 math.RT math.ATmath.KTmath.RA

Liping Li , Eric Ramos This is my paper · ORCID
classification math.RTmath.ATmath.KTmath.RA
keywords cohomologylocalcommutativedepthg-modulesalgebraapplicationauthor
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In this paper we describe a machinery for homological calculations of representations of FI_G, and use it to develop a local cohomology theory over any commutative Noetherian ring. As an application, we show that the depth introduced by the second author coincides with a more classical invariant from commutative algebra, and obtain upper bounds of a few important invariants of FI_G-modules in terms of torsion degrees of their local cohomology groups.

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Cited by 1 Pith paper

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  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.

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