FIᵐ-modules over Noetherian rings

الأصل · EN

In this paper we study representation theory of the category FIᵐ 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 FIᵐ in a natural way. In particular, we prove the representation stability property of finitely generated FIᵐ-modules over fields of characteristic 0.