# 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 $p=1$.
Keywords :
Type de document :
Pré-publication, Document de travail
6 pages, no figures. 2003

Littérature citée [10 références]

https://hal.archives-ouvertes.fr/hal-00000496
Contributeur : Rouchdi Bahloul <>
Soumis le : vendredi 11 juillet 2003 - 16:42:03
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04
Document(s) archivé(s) le : lundi 29 mars 2010 - 16:39:24

### Citation

Rouchdi Bahloul. Generic Bernstein-Sato polynomial on an irreducible affine scheme. 6 pages, no figures. 2003. 〈hal-00000496〉

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