Équations différentielles algébriques
Équations différentielles -adiques. Croissance des solutions, factorisation, indice
Equazioni differenziali -adiche e interpolazione -adica di formule classiche
We shortly introduce non-archimedean valued fields and discuss the difficulties in the corresponding theory of analytic functions. We motivate the need of -adic cohomology with the Weil Conjectures. We review the two most popular approaches to -adic analytic varieties, namely rigid and Berkovich analytic geometries. We discuss the action of Frobenius in rigid cohomology as similar to the classical action of covering transformations. When rigid cohomology is parametrized by twisting characters,...
Erratum to "Unique range sets in positive characteristic" (Acta Arith. 103 (2002), 169-189)
Espaces symétriques de Drinfeld et correspondance de Langlands locale
Espaces symétriques -adiques, mesures -adiques et transformations intégrales
Examples of ...-invariants.
Exemples de plongements d'extensions galoisiennes
Exercises dyadiques.
Existence de fonctions croulantes
Existence of and computation of integral bases
Explicit Bernstein identities and singularities of generalized Riesz integrals. (Identités de Bernstein explicites et singularités des intégrales de Riesz généralisées.)
Explicit deformation of Galois representations.
Explicit form of the modular equation.
Explicit reciprocity laws for Lubin-Tate modules.
Explicit reciprocity laws on relative Lubin-Tate groups
Exploring the -Riemann zeta function and -Bernoulli polynomials.
Exposants de Lojasiewicz dans le cas semi-algebrique p-adique
We prove the rationality of the Łojasiewicz exponent for p-adic semi-algebraic functions without compactness hypothesis. In the parametric case, we show that the parameter space can be divided into a finite number of semi-algebraic sets on each of which the Łojasiewicz exponent is constant.
Extensions de Lie et groupes d'automorphismes de corps locaux
Extensions galoisiennes d'un corps local à groupes d'inertie cycliques.