论文标题
倾斜复合物和编成符号功能
Tilting complexes and codimension functions over commutative noetherian rings
论文作者
论文摘要
在换向Noetherian环的派生类别中，我们明确构建了与满足“切片”条件的Zariski光谱的每个SP滤波相关的锡对象。我们的新结构是基于当地的共同体学，它使我们能够研究淤积物体何时倾斜。对于接收双重化复合物的环，当SP滤光到频谱上的编成拟疑函数时，这恰恰发生。在没有双重化复合物的情况下，情况更加精致，倾斜特性与环是Cohen-Macaulay环的同态图像的条件密切相关。我们还在宇宙案例中提供了结果的双重版本。
In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the "slice" condition. Our new construction is based on local cohomology and it allows us to study when the silting object is tilting. For a ring admitting a dualizing complex, this occurs precisely when the sp-filtration arises from a codimension function on the spectrum. In the absence of a dualizing complex, the situation is more delicate and the tilting property is closely related to the condition that the ring is a homomorphic image of a Cohen-Macaulay ring. We also provide dual versions of our results in the cosilting case.
