Roots of Bernstein-Sato polynomials for monomial ideals: a positive characteristic approach
The authors describe the roots of the Bernstein-Sato polynomial ideals of a monomial ideal.They prove the existence of the Bernstein-Sato polynomial for monomial ideals and study the invariants and there is given a polynomial formula for these invariants depending on a congruence mod \(p\). Note that all roots of the Bernstein-Sato polynomial of a monomial ideal are detected by this method. He also mention a geometric description of the images in \({\mathbb Q}/{\mathbb Z}\) of the roots of the Bernstein-Sato polynomials. The proofs are based on properties of the Newton polyhedron and techniques developed by the authors in two forthcoming papers (to appear in Commun. Algebra, respectively Compos. Math.). There are discussed several examples.
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