论文标题
奇异性类别的歼灭者和尺寸
Annihilators and dimensions of the singularity category
论文作者
论文摘要
让r成为一个可交换的noetherian戒指。我们证明，如果R要么是在一个完美场上有限的等准有限生成的代数，要么是具有完美残基领域的等均等等效性的完整局部环，然后是R的奇异性类别的nihihihihihihitator与jacobian Rexept of R to to to to to to to to to to to to to to to to to to to to to to hadical to to to to to to to to to to to to hadical。在某些轻度假设下，我们建立了R的nimarighit性类别的an灭者与R的共同歼灭者之间的关系。最后，我们为具有孤立的奇异性的等值出色的优质局部环的奇异性类别的维度提供了上限。这将道和高桥的结果扩展到非Cohen-Macaulay环。
Let R be a commutative noetherian ring. We prove that if R is either an equidimensional finitely generated algebra over a perfect field, or an equidimensional equicharacteristic complete local ring with a perfect residue field, then the annihilator of the singularity category of R coincides with the Jacobian ideal of R up to radical. We establish a relation between the annihilator of the singularity category of R and the cohomological annihilator of R under some mild assumptions. Finally, we give an upper bound for the dimension of the singularity category of an equicharacteristic excellent local ring with isolated singularity. This extends a result of Dao and Takahashi to non Cohen-Macaulay rings.
