Depth and the local cohomology of FIG-modules

Liping Li; Eric Ramos

doi:10.1016/j.aim.2018.02.029

Depth and the local cohomology of FI_G-modules

Liping Li
, Eric Ramos

Department of Mathematical Sciences

Hunan Normal University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

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 in [16] 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.

Original language	English
Pages (from-to)	704-741
Number of pages	38
Journal	Advances in Mathematics
Volume	329
DOIs	https://doi.org/10.1016/j.aim.2018.02.029
State	Published - 30 Apr 2018

Keywords

FI-modules
Local cohomology
Representation stability

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10.1016/j.aim.2018.02.029

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@article{9327155a22da4f8e8615627980721459,

title = "Depth and the local cohomology of FIG-modules",

abstract = "In this paper we describe a machinery for homological calculations of representations of FIG, 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 in [16] coincides with a more classical invariant from commutative algebra, and obtain upper bounds of a few important invariants of FIG-modules in terms of torsion degrees of their local cohomology groups.",

keywords = "FI-modules, Local cohomology, Representation stability",

author = "Liping Li and Eric Ramos",

note = "Publisher Copyright: {\textcopyright} 2018",

year = "2018",

month = apr,

day = "30",

doi = "10.1016/j.aim.2018.02.029",

language = "English",

volume = "329",

pages = "704--741",

}

TY - JOUR

T1 - Depth and the local cohomology of FIG-modules

AU - Li, Liping

AU - Ramos, Eric

PY - 2018/4/30

Y1 - 2018/4/30

N2 - In this paper we describe a machinery for homological calculations of representations of FIG, 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 in [16] coincides with a more classical invariant from commutative algebra, and obtain upper bounds of a few important invariants of FIG-modules in terms of torsion degrees of their local cohomology groups.

AB - In this paper we describe a machinery for homological calculations of representations of FIG, 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 in [16] coincides with a more classical invariant from commutative algebra, and obtain upper bounds of a few important invariants of FIG-modules in terms of torsion degrees of their local cohomology groups.

KW - FI-modules

KW - Local cohomology

KW - Representation stability

UR - https://www.scopus.com/pages/publications/85042519865

UR - https://www.scopus.com/pages/publications/85042519865#tab=citedBy

U2 - 10.1016/j.aim.2018.02.029

DO - 10.1016/j.aim.2018.02.029

M3 - Article

AN - SCOPUS:85042519865

SN - 0001-8708

VL - 329

SP - 704

EP - 741

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Depth and the local cohomology of FI_G-modules

Abstract

Keywords

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