Bernstein–sato Roots for Monomial Ideals in Positive Characteristic

Following work of Mustaţȃ 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 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.

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Bernstein-Sato theory for singular rings in positive characteristic

Jeffries

Núñez-Betancourt²,

Quinlan-Gallego

2023

Trans. Amer. Math. Soc.

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The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to various algebraic and topological aspects of the singularities of the vanishing locus. Work of Mustaţă, later extended by Bitoun and the third author, provides an analogous Bernstein-Sato theory for regular rings of positive characteristic. In this paper, we extend this theory to singular ambient rings in positive characteristic. We establish finiteness and rationality results for Bernstein-Sato roots for large classes of singular rings, and relate these roots to other classes of numerical invariants defined via the Frobenius map. We also obtain a number of new results and simplified arguments in the regular case.

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Bernstein–sato Roots for Monomial Ideals in Positive Characteristic

Cited by 4 publications

References 23 publications

Bernstein-Sato Polynomials in Commutative Algebra

Bernstein-Sato Polynomials in Commutative Algebra

Bernstein–sato Roots for Monomial Ideals in Positive Characteristic

Bernstein-Sato theory for singular rings in positive characteristic

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