Title :

Specializations of indecomposable polynomials

Author(s) :

Bodin, Arnaud [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Chèze, Guillaume [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Dèbes, Pierre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Manuscripta mathematica

Pages :

391-403

Publisher :

Springer Verlag

Publication date :

2012

ISSN :

0025-2611

English keyword(s) :

indecomposable polynomials
irreducible polynomials

HAL domain(s) :

Mathématiques [math]/Algèbre commutative [math.AC]
Mathématiques [math]/Géométrie algébrique [math.AG]
Mathématiques [math]/Théorie des nombres [math.NT]
Mathématiques [math]/Anneaux et algèbres [math.RA]

English abstract : [en]

We address some questions concerning indecomposable polynomials and their behaviour under specialization. For instance we give a bound on a prime $p$ for the reduction modulo $p$ of an indecomposable polynomial $P(x)\in ...
Show more >We address some questions concerning indecomposable polynomials and their behaviour under specialization. For instance we give a bound on a prime $p$ for the reduction modulo $p$ of an indecomposable polynomial $P(x)\in \Zz[x]$ to remain indecomposable. We also obtain a Hilbert like result for indecomposability: if $f(t_1,\ldots,t_r,x)$ is an indecomposable polynomial in several variables with coefficients in a field of characteristic $p=0$ or $p>\deg(f)$, then the one variable specialized polynomial $f(t_1^\ast+\alpha_1^\ast x,\ldots,t_r^\ast+\alpha_r^\ast x,x)$ is indecomposable for all $(t_1^\ast, \ldots, t_r^\ast, \alpha_1^\ast, \ldots,\alpha_r^\ast)\in \overline k^{2r}$ off a proper Zariski closed subset.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL