Ascending chain condition for $F$ -pure thresholds on a fixed strongly $F$ -regular germ
Ascending chain condition for $F$ -pure thresholds on a fixed strongly $F$ -regular germ
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DOI：
10.1112/s0010437x19007358
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发表时间：
2017-10
影响因子：
1.8
通讯作者：
Kenta Sato
中科院分区：
文献类型：
--
作者：
Kenta Sato
证明了强$F$正则对的固定芽上的所有$F$纯阈值的集合满足升链条件。作为一个推论，我们验证了光滑变异上的所有$F$纯阈值集合的升链条件，或者更一般地说，在具有驯服商奇点的变异上，这是对Blickle， Mustaţǎ和Smith的猜想的肯定回答。
In this paper, we prove that the set of all $F$ -pure thresholds on a fixed germ of a strongly $F$ -regular pair satisfies the ascending chain condition. As a corollary, we verify the ascending chain condition for the set of all $F$ -pure thresholds on smooth varieties or, more generally, on varieties with tame quotient singularities, which is an affirmative answer to a conjecture given by Blickle, Mustaţǎ and Smith.