Year: 2026
Type: preprint
Abstract: Generic categories arising in representation stability and equivariant commutative algebra are difficult to analyze in positive characteristic, as these categories rarely admit enough (or even any) finitely generated injectives. Our main observation is that they are nonetheless an increasing union of Serre subcategories, each with finitely many simples and enough finite length injectives. We package this into an axiomatic framework which is widely applicable. In particular, we use this to analyze (1) VI-modules in non-describing characteristic, recovering Nagpal's classification of simple generic VI-modules, and (2) GL-equivariant modules over truncated polynomial rings and exterior algebras in infinitely many variables.
Source: arXiv (Cornell University)
Author: Ganapathy, Karthik
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206203642