A remark on FI-module homology
Wee Liang Gan, Liping Li
TL;DR
This paper demonstrates that FI-homology can be computed using a Koszul complex and establishes a key regularity property of finitely generated torsion FI-modules, linking their regularity to their degree.
Contribution
It introduces a Koszul complex approach for FI-homology computation and proves a fundamental regularity equality for finitely generated torsion FI-modules.
Findings
FI-homology can be computed via a Koszul complex
Castelnuovo-Mumford regularity equals the degree for finitely generated torsion FI-modules
Provides a new method for analyzing FI-modules
Abstract
We show that the FI-homology of an FI-module can be computed via a Koszul complex. As an application, we prove that the Castelnuovo-Mumford regularity of a finitely generated torsion FI-module is equal to its degree.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications