#### Vol. 13, No. 9, 2019

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VI-modules in nondescribing characteristic, part I

### Rohit Nagpal

Vol. 13 (2019), No. 9, 2151–2189
##### Abstract

Let VI be the category of finite dimensional ${\mathbb{F}}_{q}$-vector spaces whose morphisms are injective linear maps and let $k$ be a noetherian ring. We study the category of functors from VI to $k$-modules in the case when $q$ is invertible in $k$. Our results include a structure theorem, finiteness of regularity, and a description of the Hilbert series. These results are crucial in the classification of smooth irreducible ${GL}_{\infty }\left({\mathbb{F}}_{q}\right)$-representations in nondescribing characteristic which is contained in Part II of this paper (VI-modules in nondescribing characteristic, part II, arxiv:1810.04592).

##### Keywords
VI-modules, FI-modules, finite general linear groups, representation stability
##### Mathematical Subject Classification 2010
Primary: 20C33
Secondary: 13D45, 20J05