Ascending Chain Condition for F-Pure Thresholds with Fixed Embedding Dimension
Ascending Chain Condition for F-Pure Thresholds with Fixed Embedding Dimension
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DOI：
10.1093/imrn/rnz031
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发表时间：
2018-05
影响因子：
1
通讯作者：
Kenta Sato
中科院分区：
文献类型：
--
作者：
Kenta Sato
本文证明了具有固定嵌入维数的所有$F$纯理想阈值的集合满足升链条件。作为一个推论，给定一个整数$d$，我们验证了所有$d$维正规局部完全交变上的所有$F$纯阈值集合的升链条件。在证明这些结果的过程中，我们也证明了非强正则对上的纯理想阈值的合理性。
In this paper, we prove that the set of all $F$-pure thresholds of ideals with fixed embedding dimension satisfies the ascending chain condition. As a corollary, given an integer $d$, we verify the ascending chain condition for the set of all $F$-pure thresholds on all $d$-dimensional normal locally complete intersection varieties. In the process of proving these results, we also show the rationality of $F$-pure thresholds of ideals on non-strongly $F$-regular pairs.