Local cohomology and the multi-graded regularity of FI$^m$-modules
Representation Theory
2017-11-22 v1 Commutative Algebra
Algebraic Topology
Combinatorics
Abstract
We develop a local cohomology theory for FI-modules, and show that it in many ways mimics the classical theory for multi-graded modules over a polynomial ring. In particular, we define an invariant of FI-modules using this local cohomology theory which closely resembles an invariant of multi-graded modules over Cox rings defined by Maclagan and Smith. It is then shown that this invariant behaves almost identically to the invariant of Maclagan and Smith.
Cite
@article{arxiv.1711.07964,
title = {Local cohomology and the multi-graded regularity of FI$^m$-modules},
author = {Liping Li and Eric Ramos},
journal= {arXiv preprint arXiv:1711.07964},
year = {2017}
}