Local cohomology and the multi-graded regularity of FI^m-modules

Liping Li Hunan Normal University Eric Ramos U. Michigan

K-Theory and Homology Representation Theory Rings and Algebras mathscidoc:1711.20002

We develop a local cohomology theory for FI^m-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^m-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.
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  title={Local cohomology and the multi-graded regularity of FI^m-modules},
  author={Liping Li, and Eric Ramos},
Liping Li, and Eric Ramos. Local cohomology and the multi-graded regularity of FI^m-modules. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171123171714744252859.
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