ANNIHILATORS AND DIMENSIONS OF THE SINGULARITY CATEGORY

IF 0.8 2区 数学 Q2 MATHEMATICS Nagoya Mathematical Journal Pub Date : 2022-02-19 DOI:10.1017/nmj.2022.45
Jian Liu
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引用次数: 1

Abstract

Abstract 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 relationship 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.
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湮灭子和奇点范畴的维度
设R是一个交换诺瑟环。证明了如果R是一个完全域上的等维有限生成代数,或者是一个具有完全剩余域的等维等特征完备局部环,则R的奇异范畴的湮灭子与R的雅可比理想直至根号重合。在一些温和的假设下,我们建立了R的奇异范畴的湮灭子与R的上同湮灭子之间的关系。最后给出了具有孤立奇点的等特征优局部环奇点范畴维数的上界。这将Dao和Takahashi的结果扩展到非cohen - macaulay环。
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
31
审稿时长
6 months
期刊介绍: The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.
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