# Generic Bernstein-Sato polynomial on an irreducible affine scheme

Abstract : Given $p$ polynomials with coefficients in a commutative unitary integral ring $\mathcal{C}$ containing $\mathbb{Q}$, we define the notion of a generic Bernstein-Sato polynomial on an irreducible affine scheme $V \subset \text{Spec}(\mathcal{C})$. We prove the existence of such a non zero rational polynomial which covers and generalizes previous existing results byH. Biosca. When $\mathcal{C}$ is the ring of an algebraic or analytic space, we deduce a stratification of the space of the parameters such that on each stratum, there is a non zero rational polynomial which is a Bernstein-Sato polynomial for any point of the stratum. This generalizes a result of A. Leykin obtained in the case $p=1$.
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https://hal.archives-ouvertes.fr/hal-00000496
Contributor : Rouchdi Bahloul <>
Submitted on : Friday, July 11, 2003 - 4:42:03 PM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM
Long-term archiving on: : Monday, March 29, 2010 - 4:39:24 PM

### Citation

Rouchdi Bahloul. Generic Bernstein-Sato polynomial on an irreducible affine scheme. 2003. ⟨hal-00000496⟩

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