Réalisation de Hodge des motifs de Voevodsky

Sur un sous-corps du corps des complexes, nous associons à un objet de la catégorie des motifs géométriques de Voevodsky un Z-complexe de Hodge mixte de Deligne (Inst Hautes études Sci Publ Math 44:5–77, [D74]). Les filtrations par le poids et de Hodge sont représentées par des foncteurs de troncature, d’un complexe des poids à la Bondarko (J K-Theory 6(3):387–504, [Bo10a]) pour la première et troncature du complexe de De Rham (Lecomte Wach, Manuscr Math 129:75–90, [LW09]) pour l’autre.     

Non-trivialité des points de Heegner

We give here a second proof of Mazur's conjecture on higher Heegner points, using a proven case of the André–Oort conjecture as a substitute for the main ingredient of our first proof [1], a theorem of M. Ratner. To cite this article: C. Cornut, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1039–1042.     

Uniformisation de l’espace des feuilles de certains feuilletages de codimension un

This paper deals with codimension one (may be singular) foliations on compact Kälher manifoldswhose conormal bundle is assumed to be pseudo-effective. Using currents with minimal singularities, we show that one can endow the space of leaves with a metric of constant non positive curvature wich may degenerate on a “rigidly” embedded invariant hypersurface.     

à propos de l’indice de composition des nombres

 We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,

À propos de l’indice de composition des nombres

 We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,

Equirépartition des coefficients de Fourier des fonctions L de carrés et de cubes symétriques

Dans ce travail, on étudie l’équirépartition et l’équirépartition harmonique des coefficients de Fourier des fonctions L de carrés et de cubes symétriques d’une forme primitive.     

Géométrie des espaces de Banach ayant des approximations de l'identité contractantes

Let a, c ≥ 0 and let B be a compact set of scalars. We introduce property M^* (a, B, c) of Banach spaces X which is a geometric property of Banach spaces generalizing property (M^*) due to Kalton. Using M^*(a, B, c) with max ¦B¦ + c > 1, we characterize intrinsically a large class of shrinking approximations of the identity, including those related to M-, u-, and h-ideals of compact operators. We also show that the existence of these approximations of the identity is separably determined. As an application, we study ideals of compact and approximable operators. In particular, this provides an alternative unified and easier approach to the theories of M-, u-, and h-ideals of compact operators.     

Geométrie des suites de Kronecker

Let Θ be a element of the d-dimensional torus $\mathbb{T}$ ^d andτ the translationτ(x)=x + Θ. When d=1 there existe some partitions of $\mathbb{T}$ ¹ which are associated withτ. We prove the existence of partitions of $\mathbb{T}$ ^d which enjoyed the same kind of properties and whose elements (A _i ) _i≤n are convex polytopes. We also give a lower bound for the isotropic discrepancy of the sequence (nΘ) _nε?.     

Existence locale de solutions c∞ pour des equations de monge-ampere changeant de type

We prove the C∞ local solvability of the n-dimensional Monge-A mpé:ere equation det (u_ij + a_ij(x,u,▽u))= K(x) f(x, u, ▽u), f> 0, in a neighborhood of any point x₀ where K(x₀)= 0 but dK(x_o) ¦0.     

Ovoßdes et Groupes de Suzuki

Sans résuméA MonsieurReinhold Baer, pour son 60e anniversaire, en témoignage d'affectueuse estime     

Spectre des réseaux de poutres

We consider the spectral analysis of a model of networks of Euler-Bernoulli beams. We first give the characteristic equation for the spectrum. Secondly, in some particular situations, we show that the spectrum depends only on the structure of the graph. Thirdly, we investigate the asymptotic behaviour of the eigenvalues by proving the so-called Weyl's formula.     

Approximation polynomiale des jets de Whitney ∂‾-plats de classe M

We study the problem of global approximation by polynomials in Whitney $\stackrel{￣}{?}$-flat jet classes on irregular compacts of ${\mathbb{C}}^N$.     

Résolution des équations de Navier-Stokes dans des espaces anisotropes

In this paper we prove the global existence and uniqueness of the solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which H^δ in the i-th direction, δ₁+δ₂+δ₃=½,½< δ_i <½ and in a space which is L² in the first two directions and B_2,1^½ in the third direction, where H and B (respectively) denote the usual homogeneous Sobolev and Besov (respectively) spaces.