诺特环的导出范畴上紧生成t-结构的分类
Classifying Compactly generated t-structures on the derived category of a Noetherian ring
摘要：
利用Spec（R）上的支集降滤子，对交换诺特环R上模的导出范畴上的复生成t-结构进行了分类.一个由支集Z：Z -> Spec（R）构成的递减过滤满足弱Cousin条件，如果对任意整数i \in Z，集合Z（i）包含Z（i+1）中每个点的所有直接推广. D^b_fg（R）（等价于D^-_fg（R））上的每个t-结构都是由D（R）上的完备生成的t-结构诱导的，这些结构的伴随支撑滤子满足弱Cousin条件。如果环R具有对偶复形，我们证明了这些复形是D^b_fg（R）上的t-结构。更一般地说，如果R有一个点态对偶复形，我们对D_fg（R）上所有对偶生成的t-结构进行分类。
英文摘要：
We classify complactly generated t-structures on the derived category of modules over a commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec(R). A decreasing filtration by supports ϕ: Z -> Spec(R) satisfies the weak Cousin condition if for any integer i \in Z, the set ϕ(i) contains all the inmediate generalizations of each point in ϕ(i+1). Every t-structure on D^b_fg(R) (equivalently, on D^-_fg(R)) is induced by complactly generated t-structures on D(R) whose associated filtrations by supports satisfy the weak Cousin condition. If the ring R has dualizing complex we prove that these are exactly the t-structures on D^b_fg(R). More generally, if R has a pointwise dualizing complex we classify all compactly generated t-structures on D_fg(R).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
