On the local cohomology of L-shaped integral FI-modules
type: Item
instance of: scholarly article
title: On the local cohomology of L-shaped integral FI-modules
author: Sophie Kriz
published in: Journal of Algebra
publication date: 2022-09-29T00:00:00Z
review text: In representation stability, representations of the category of finite sets and injections, called FI-modules, were introduced by \textit{T. Church} et al. in [Duke Math. J. 164, No. 9, 1833--1910 (2015; Zbl 1339.55004)]. For an FI-module \(M\), its torsion submodule \(TM\) is defined to consist of those elements of \(M\) which are sent to \(0\) by inclusions into large enough finite sets. An important topic in representation stability is the calculation of local cohomology, i.e., the derived functors of the FI-torsion of a given FI-module. Rationally, this was solved by \textit{S. V. Sam} and \textit{A. Snowden} (see [Trans. Am. Math. Soc. 368, No. 2, 1097--1158 (2016; Zbl 1436.13012); Forum Math. Sigma 7, Paper No. e5, 71 p. (2019; Zbl 1441.16008)]), but remain unknown integrally. In the paper under review the author compute the local cohomology of the integral Spechtral FI-module corresponding to the \(L\)-shaped Young diagrams i.e. the partitions \((2, 1, \ldots , 1)\). Furthermore the presence of torsion is discussed.
reviewed by: Egle Bettio
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 7594493
zbMATH Keywords: representation stability
zbMATH Keywords: Specht modules
zbMATH Keywords: local cohomology
zbMATH Keywords: FI-modules
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2022.08.003
OpenAlex ID: W4292136458
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DOI: 10.1016/J.JALGEBRA.2022.08.003
description: scientific article; zbMATH DE number 7594493