AI 中文总结
将Serre条件推广至Verdier型范畴，定义几何Serre条件，探讨其与perversity的关系，并证明Auslander-Reiten猜想的几何版本。
AI 中文摘要
我们将凝聚层的Serre条件推广到配备$t$-结构和对偶的三角范畴，称之为Verdier型范畴。我们给出此类范畴及其相关Serre条件的例子，然后聚焦于可构造层，在这些条件下我们称之为几何Serre条件。我们研究它们与perversity的关系，并通过一系列例子说明该理论。最后，我们证明了Auslander-Reiten猜想的几何版本。
英文摘要
We generalize Serre's conditions for coherent sheaves to triangulated categories equipped with a $t$-structure and duality, which we call Verdier-type categories. We present examples of such categories and their associated Serre conditions, then focus on constructible sheaves, where we refer to these conditions as geometric Serre conditions. We investigate their relationship with perversity and illustrate the theory through a range of examples. Finally, we prove a geometric version of the Auslander-Reiten conjecture.
Comments14 pages
