Following the work of Mustaţă and Bitoun, we recently developed a notion of Bernstein–Sato roots for arbitrary ideals, which is a prime characteristic analogue for the roots of the Bernstein–Sato polynomial. Here, we prove that for monomial ideals the roots of the Bernstein–Sato polynomial (over $\mathbb{C}$) agree with the Bernstein–Sato roots of the mod $p$ reductions of the ideal for $p$ large enough. We regard this as evidence that the characteristic-$p$ notion of Bernstein–Sato root is reasonable.

中文翻译：

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正特征单项理想的伯恩斯坦-佐藤根

在 Mustaţă 和 Bitoun 的工作之后，我们最近开发了任意理想的 Bernstein-Sato 根的概念，它是 Bernstein-Sato 多项式根的主要特征模拟。在这里，我们证明对于单项式理想，伯恩斯坦-佐藤多项式的根（超过$\mathbb{C}$) 同意 mod 的 Bernstein–Sato 根源$p$理想的减少$p$足够大。我们认为这是证明特征-$p$Bernstein-Sato 根的概念是合理的。