AI 中文总结
研究通过余挠对和阿贝尔模型结构为离散群在交换环上引入恰当稳定模范畴，此范畴是良生成张量三角范畴，与其他稳定范畴一致，并引入同调维数研究，丰富了群代数稳定模范畴理论。
AI 中文摘要
我们通过余挠对和阿贝尔模型结构为任意离散群在任意交换环上引入恰当稳定模范畴。该范畴是一个良生成张量三角范畴，当交换环正则时是紧生成的。我们的构造类似于通过恰当等变稳定同伦理论的拓扑方法。它与Mazza - Symonds稳定模范畴（只要后者有定义）以及与分层定义群相关的其他稳定范畴一致。过程中我们引入了某些同调维数并详细研究，与经典概念作比较。
英文摘要
We introduce the proper stable module category for an arbitrary discrete group over any commutative ring by means of cotorsion pairs and abelian model structures. This category is a well-generated tensor-triangulated category and is compactly generated in case the commutative ring is regular. Our construction resembles the topological approach via proper equivariant stable homotopy theory. Moreover, it agrees with the Mazza-Symonds stable module category, whenever the latter is defined, and with various other stable categories associated to hierarchically defined groups. Along the way, we introduce certain homological dimensions and study them in detail, comparing them with the classical notions.
Comments31 pages
