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

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Cited by in corpus (4)

• Local cohomology and the multi-graded regularity of FI${}^m$-modules
• Representation stability and arithmetic statistics of spaces of 0-cycles
• Castelnuovo-Mumford regularity of representations of certain product categories
• Asymptotic behaviors of representations of graded categories with inductive functors