Approximation des schémas en groupes, quasi compacts sur un corps
Approximation diophantienne dans les corps de séries en plusieurs variables
Nous montrons ici un théorème d’approximation diophantienne entre le corps des séries formelles en plusieurs variables et son complété pour la topologie de Krull.
Approximation diophantienne dans les groupes algébriques commutatifs. (I): Une version effective du théorème du sous-group algébrique.
Approximation diophantienne sur les variétés semi-abéliennes
Approximation faible aux places de bonne réduction sur les surfaces cubiques sur les corps de fonctions
On démontre que les surfaces cubiques lisses sur les corps de fonctions d’une courbe sur un corps algébriquement clos de caractéristique vérifient l’approximation faible aux places de bonne réduction. La méthode utilisée imite celle employée par Swinnerton-Dyer [10] dans le cas des corps de nombres.
Approximation of -functions without changing their zero-set
For a function (where is a real algebraic manifold) the following problem is studied. If is an algebraic subvariety of , can be approximated by rational regular functions such that We find that this is possible if and only if there exists a rational regular function such that and g(x) for any in . Similar results are obtained also in the analytic and in the Nash cases.For non approximable functions the minimal flatness locus is also studied.
Approximation of holomorphic maps by algebraic morphisms
Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.
Approximation Properties and Existential Completeness for Ring Morphisms.
Approximations diophantiennes -adiques sur les courbes elliptiques admettant une multiplication complexe
Approximations simultanées sur les groupes algébriques commutatifs
Arakelov Chow groups of abelian schemes, arithmetic Fourier transform, and analogues of the standard conjectures of Lefschetz type.
Arakelov computations in genus curves
Arakelov invariants of arithmetic surfaces are well known for genus 1 and 2 ([4], [2]). In this note, we study the modular height and the Arakelov self-intersection for a family of curves of genus 3 with many automorphisms:Arakelov calculus involves both analytic and arithmetic computations. We express the periods of the curve in terms of elliptic integrals. The substitutions used in these integrals provide a splitting of the jacobian of as a product of three elliptic curves. Using the corresponding...
Arakelov invariants of Riemann surfaces.
Arakelov's Theorem for Abelian Varieties.
Arc-analyticity and polynomial arcs
We relate the notion of arc-analyticity and the one of analyticity on restriction to polynomial arcs and we prove that in the subanalytic setting, these two notions coincide.
Arcs analytiques et résolution minimale des singularités des surfaces quasi homogènes
Are rational curves determined by tangent vectors?
Let be a projective variety which is covered by rational curves, for instance a Fano manifold over the complex numbers. In this paper, we give sufficient conditions which guarantee that every tangent vector at a general point of is contained in at most one rational curve of minimal degree. As an immediate application, we obtain irreducibility criteria for the space of minimal rational curves.
Are the Isolated Singularities of Complete Intersections Determined by Their Singular Subspaces?
Arithmetic and geometry of the curve y³+1=x⁴
Arithmetic characteristic classes of automorphic vector bundles.