Essential dimension: A functorial point of view (after A. Merkurjev).
Estensioni di una struttura paracomplessa su un corpo algebricamente chiuso ad un suo ampliamento trascendente semplice
Étienne Bézout : analyse algébrique au siècle des lumières
Le but de cet article, à travers l’étude des travaux en analyse algébrique finie d’Étienne Bézout (1730-1783), est de mieux faire connaître ses résultats, tels qu’il les a effectivement trouvés, et de mettre en valeur aussi bien les points de vue novateurs que les méthodes originales, mis en œuvre à cet effet. L’idée de ramener le problème de l’élimination d’une ou plusieurs inconnues à l’étude d’un système d’équations du premier degré, son utilisation inhabituelle des coefficients indéterminés...
Euclidean function fields.
Euclidean Number Fields of Large Degree
Euklidische Körper und euklidische Hüllen von Körpern.
Évariste Galois and the social time of mathematics
The thrust of this article is to offer a new approach to the study of Galois’s Mémoire sur les conditions de résolubilité des équations par radicaux. Drawing on methodology developed by social and cultural historians, it contextualizes Galois’s work by situating it in the parisian mathematical milieu of the 1820s and 1830s. By reconstructing the social process whereby a young man became an established mathematician at the time, this article shows that Galois’s trajectory was far from unusual, and...
Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials
2000 Mathematics Subject Classification: 12D10.In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs.Research partially supported by research project 20682 for cooperation...
Every reasonably sized matrix group is a subgroup of S ∞
Every reasonably sized matrix group has an injective homomorphism into the group of all bijections of the natural numbers. However, not every reasonably sized simple group has an injective homomorphism into .
Exact Solution of Linear Equations Using P-Adic Expansions
Exercises dyadiques.
Existence de fonctions croulantes
Existentially closed domains with radical relations.
Explicit formulas for strong Davenport pairs
Explicit solutions to embedding problems associated to orthogonal Galois representations.
Exposants de la monodromie -adique et structure de Frobenius pour des équations différentielles
Dans cet article nous présentons la théorie des équations différentielles -adiques et ses applications concernant le théorème de finitude de la cohomologie -adique d’une variété affine et le théorème de la monodromie -adique des représentations galoisiennes locales.
Exposants, irrégularités et multiplicités
Exposants -adiques et théorèmes d’indice pour les équations différentielles -adiques
Extending automorphisms to the rational fractions field.
We say that a field K has the Extension Property if every automorphism of K(X) extends to an automorphism of K. J.M. Gamboa and T. Recio [2] have introduced this concept, naive in appearance, because of its crucial role in the study of homogeneity conditions in spaces of orderings of functions fields. Gamboa [1] has studied several classes of fields with this property: Algebraic extensions of the field Q of rational numbers; euclidean, algebraically closed and pythagorean fields; fields with an...
Extending Hardy fields by non--germs
For a large class of Hardy fields their extensions containing non--germs are constructed. Hardy fields composed of only non--germs, apart from constants, are also considered.