发表机构
University of California, San Diego（加利福尼亚大学圣地亚哥分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对正特征下通用范畴缺乏足够有限生成内射对象的难题，构建适用的公理化框架，分析VI-模分类及GL-等变模相关问题，重现已有分类结果。
AI 中文摘要
在正特征下，由表示稳定性与等变交换代数产生的通用范畴难以分析，因为这类范畴很少具有足够的（甚至完全没有）有限生成内射对象。我们的主要发现是，这类范畴仍是Serre子范畴的递增并，每个Serre子范畴具有有限个单对象及足够的有限长度内射对象。我们将这一结论整合为适用性广泛的公理化框架，并用其分析两类问题：（1）非定义特征下的VI-模，重现Nagpal关于单通用VI-模的分类；（2）无限多个变量的截断多项式环与外代数上的GL-等变模。
英文摘要
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.
Comments21 pages, no figures
