# Bernstein-Sato roots for monomial ideals in positive characteristic

## TL;DR

This paper demonstrates that for monomial ideals, the Bernstein-Sato roots in characteristic zero match those in large prime characteristic, supporting the validity of the positive characteristic Bernstein-Sato root concept.

## Contribution

It establishes the equivalence of Bernstein-Sato roots in characteristic zero and large prime characteristic for monomial ideals, validating the positive characteristic approach.

## Key findings

- Bernstein-Sato roots in characteristic zero match mod-p roots for large p
- Supports the validity of positive characteristic Bernstein-Sato roots
- Extends understanding of Bernstein-Sato roots in algebraic geometry

## Abstract

Following work of Musta\c{t}\u{a} 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.