标题： 均匀主导局部环和奇点范畴的Orlov谱 显示英文标题

标题： Uniformly dominant local rings and Orlov spectra of singularity categories

摘要： 我们定义一个均匀主导局部环为一个交换诺特局部环，其包含一个整数 r，使得剩余域可以通过奇异范畴中的任何非零对象通过直和项、移位和最多 r 个映射圆锥来构建。 我们找到均匀主导的充分条件，借此我们证明 Burch 环和具有准分解极大理想的局部环是均匀主导的。 对于一个均匀主导的优秀等特征孤立奇点，我们得到了奇异范畴的 Orlov 谱的一个上界。 我们证明均匀主导性在基本运算下保持不变，并给出了构造均匀主导局部环的技术。 我们还提供了将这些方法应用于具有可分解极大理想的局部环的示例。 显示英文摘要

摘要： We define a uniformly dominant local ring as a commutative noetherian local ring with an integer r such that the residue field is built from any nonzero object in the singularity category by direct summands, shifts and at most r mapping cones. We find sufficient conditions for uniform dominance, by which we show Burch rings and local rings with quasi-decomposable maximal ideal are uniformly dominant. For a uniformly dominant excellent equicharacteristic isolated singularity, we get an upper bound of the Orlov spectrum of the singularity category. We prove uniform dominance is preserved under basic operations, and give techniques to construct uniformly dominant local rings. An application of our methods to local rings with decomposable maximal ideal is provided as well.