Corpus ID: 235446629

Bernstein-Sato polynomials in commutative algebra

@inproceedings{Montaner2021BernsteinSatoPI,
  title={Bernstein-Sato polynomials in commutative algebra},
  author={J. {\`A}. Montaner and Jack Jeffries and Luis N'unez-Betancourt},
  year={2021}
}
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra. 

References

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We give a combinatorial description of the roots of the Bernstein–Sato polynomial of a monomial ideal using the Newton polyhedron and some semigroups associated to the ideal.
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TLDR
This paper compares the approach of Briancon and Maisonobe for computing Bernstein–Sato ideals with the readily available method of Oaku and Takayama and shows that it can deal with interesting examples that have proved intractable so far. Expand
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We prove a conjecture of the first author relating the Bernstein-Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. ThisExpand
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We generalize the Bernstein-Sato polynomials of Budur, Mustata and Saito to ideals in normal semigroup rings. In the case of monomial ideals, we also relate the roots of the Bernstein-Sato polynomialExpand
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We describe the roots of the Bernstein-Sato polynomial of a monomial ideal using reduction mod p and invariants of singularities in positive chracteristic. We give in this setting a positive answerExpand
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Algorithm for Computing Bernstein-Sato Ideals Associated with a Polynomial Mapping
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TLDR
The aim is to present an algorithm for computing generators of Bjand B? of functional equations and related ideals called Bernstein?Sato ideals using standard basis techniques. Expand
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Musta\c{t}\u{a} defined Bernstein-Sato polynomials in prime characteristic for principal ideals and proved that the roots of these polynomials are related to the $F$-jumping numbers of the ideal.Expand
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