Diophantine approximations on projective spaces.
Direct images in non-archimedean Arakelov theory
We develop a formalism of direct images for metrized vector bundles in the context of the non-archimedean Arakelov theory introduced in our joint work with S. Bloch. We prove a Riemann-Roch-Grothendieck theorem for this direct image.
Direct Images of Sheaves of Differentials and the Atiyah Class.
Directional properties of sets definable in o-minimal structures
In a previous paper by Koike and Paunescu, it was introduced the notion of direction set for a subset of a Euclidean space, and it was shown that the dimension of the common direction set of two subanalytic subsets, called the directional dimension, is preserved by a bi-Lipschitz homeomorphism, provided that their images are also subanalytic. In this paper we give a generalisation of the above result to sets definable in an o-minimal structure on an arbitrary real closed field. More precisely, we...
Dirichlet and Neumann problems for string equation, Poncelet problem and Pell-Abel equation.
Dirichlet motives via modular curves
Discrete groups, Mumford curves and Theta functions
Discrete polymatroids.
Discriminant d’un germe et quotients de contact dans la résolution de
Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5
∗ Research partially supported by INTAS grant 97-1644A real polynomial of one real variable is hyperbolic (resp. strictly hyperbolic) if it has only real roots (resp. if its roots are real and distinct). We prove that there are 116 possible non-degenerate configurations between the roots of a degree 5 strictly hyperbolic polynomial and of its derivatives (i.e. configurations without equalities between roots). The standard Rolle theorem allows 286 such configurations. To obtain the result we study...
Discriminants of etale algebras and related structures.
Discussion de l'intersection de deux surfaces du second ordre
Discussion de l'intersection de deux surfaces du second ordre
Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall.
Diskriminanten und Picard-Invarianten freier quadratischer Erweiterungen.
Dissimilarity vectors of trees are contained in the tropical Grassmannian.
Distance géodésique sur un sous-analytique.
Pour un ensemble sous-analytique, connexe fermé, la distance géodésique est atteinte et est uniformément équivalente, avec des constantes arbitrairement proches de 1, à une distance sous-analytique.
Distance preserving mappings of Grassmann graphs.
Distances on the tropical line determined by two points
Let and be points in . Write if is a multiple of . Two different points and in uniquely determine a tropical line passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on leaves. It is also a metric graph. If some representatives and of and are the first and second columns of some real normal idempotent order matrix , we prove that the tree is described by a matrix , easily obtained from . We also prove that...
Distinguishing Prymians from Jacobians.