本项目以交换代数中的相关理论为工具，研究交换诺特环的导出范畴中的紧生成 t-结构与 silting 理论。首先，在分次交换诺特环上，建立齐次素谱的 specialization 封闭子集的过滤与无界导出范畴中具有某种与张量理想相关属性的紧生成 t-结构间的双射对应。其次，探讨 silting 复形在与交换诺特环 R 上正则元相关环同态下的“升”和“降”性质。接下来，凭借与极大理想相关的余局部化理论对无界导出范畴 D(R) 中余 silting 复形进行分类。最后，借助 Zariski 谱中 specialization 封闭子集的有界过滤，建立 D(R) 中 silting pair 的等价刻画，并借此讨论 silting pair 的相关问题。本项目的研究对促进导出范畴中 t-结构与 silting 理论的发展具有重要意义。

We study compactly generated t-structures and silting theory in derived categories over commutative Noetherian rings via relevant theory in commutative algebra. Firstly, we will establish, over a graded commutative Noetherian ring, a bijective correspondence between filtrations by specialization closed subsets in the homogeneous spectrum and compactly generated t-structures which possess certain properties related to tenser ideals. Secondly, we discuss, over a commutative Noetherian ring R,“ascent” and “descent” properties of silting complexes along ring homomorphisms with respect to a regular element on R. Thirdly, cosilting complexes in the unbounded derived category D(R) will be classified by the colocalization theory related to maximal ideals of R. Finally, we establish an equivalent characterization of a silting pair in D(R) via certain a bounded filtration by specialization closed subsets of the Zariski spectrum of R. By such a characterization, some problems related to a silting pair will also be discussed. The study of the project will play an important role in developing t-structures and silting theory in derived categories.