希尔伯特-塞缪尔函数的恒定性

IF 0.8 2区数学 Q2 MATHEMATICS

Nagoya Mathematical Journal Pub Date : 2024-05-24 DOI:10.1017/nmj.2024.13

VINCENT COSSART, OLIVIER PILTANT, BERND SCHOBER

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引用次数: 0

摘要

我们证明了一个关于局部诺特方案的希尔伯特-萨缪尔函数恒定性的标准，这种方案的局部环在每一点上都是优秀的。更准确地说，我们证明了当且仅当方案沿其还原方向通常是平坦的，且还原本身是正则时，希尔伯特-萨缪尔函数在这样的方案上是局部恒定的。底层还原方案的规则性是一个重要的新特性。

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CONSTANCY OF THE HILBERT–SAMUEL FUNCTION

We prove a criterion for the constancy of the Hilbert–Samuel function for locally Noetherian schemes such that the local rings are excellent at every point. More precisely, we show that the Hilbert–Samuel function is locally constant on such a scheme if and only if the scheme is normally flat along its reduction and the reduction itself is regular. Regularity of the underlying reduced scheme is a significant new property.

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来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

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.