-adic analysis and classical sequences of numbers. (Analyse -adique et suites classiques de nombres.)
-adic difference-difference Lotka-Volterra equation and ultra-discrete limit.
-adic Siegel halfspace
-adic Teichmüller space and Siegel halfspace
-adic Teichmuller space for genus
-extensions abéliennes
PAC fields over number fields
We prove that if is a number field and is a Galois extension of which is not algebraically closed, then is not PAC over .
p-Adic L-Functions for CM Fields.
P-adic root isolation.
We present an implemented algorithmic method for counting and isolating all p-adic roots of univariate polynomials f over the rational numbers. The roots of f are uniquely described by p-adic isolating balls, that can be refined to any desired precision; their p-adic distances are also computed precisely. The method is polynomial space in all input data including the prime p. We also investigate the uniformity of the method with respect to the coefficients of f and the primes p. Our method thus...
p-adic semi-algebraic sets and cell decomposition.
Parallélogrammes galoisiens infinis
Pathological functions on Puiseux series ordered fields and others.
Periodic points, multiplicities, and dynamical units.
Perspective historique sur les rapports entre la théorie des modèles et l’algèbre. Un point de vue tendancieux
Je vais traiter, d’un point de vue personnel, la naissance et les premiers développements de la théorie des modèles pendant la période qui s’étend de sa naissance vers 1870, avec les travaux de Peirce, jusqu’au théorème de Morley vers 1965. J’insisterai particulièrement sur l’aspect « algèbre universelle » et j’essaierai de dégager comment la notion de définissabilité a fait évoluer cette théorie jusqu’à une science complexe pouvant apporter de nouvelles idées au reste des mathématiques.
Pfister's conjecture on quadratic Co-fields.
Pfister's Dimension and the Level of Fields.
p-Henselian fields.
Picard-Vessiot theory in general Galois theory
We give a transparent proof that difference Picard-Vessiot theory is a part of the general difference Galois theory. We apply the proof to iterative q-difference Picard-Vessiot theory to show that Picard-Vessiot theory for iterative q-difference field extensions is in the scope of the general Galois theory of Heiderich. We also show that Picard-Vessiot theory is commutative in the sense that studying linear difference-differential equations, no matter how twisted the operators are, we cannot encounter...
Places of alternative fields
Plongeants d'extensions galoisiennes