FI${}^m$-modules over Noetherian rings

Abstract

In this paper we study representation theory of the category FI${}^m$ introduced by Gadish which is a product of copies of the category FI, and show that quite a few interesting representational and homological properties of FI can be generalized to FI${}^m$ in a natural way. In particular, we prove the representation stability property of finitely generated FI${}^m$-modules over fields of characteristic 0.

A few remarks added in Section 1. Several typos corrected

References in corpus (2)

• FI-modules and the cohomology of modular representations of symmetric groups
• Bounding the homology of FI-modules

Cited by in corpus (2)

• Local cohomology and the multi-graded regularity of FI${}^m$-modules
• Representation stability and arithmetic statistics of spaces of 0-cycles