Courants positifs à supports dans une bande

Let T be a positive current of bidimension $(p,p)$ on ${\mathbb{C}}^n$ with support in a strip. If T is closed, S. Giret has proved that T admits a well defined lifting through a blow up with smooth center. The class of positive closed currents with bidimension $(1,1)$ in the unit bidisc ${\Delta }^2$ and with support in a strip, plays a central role in the study of the dynamics of some holomorphic maps. In this note, we prove some estimates of the trace measure of T when $d{d}^{c}T?0$, we prove in particular that if T is closed, then it is algebraic. We then prove two support theorems; the first one in the case where the degree of T is finite and the second in the case where T is positive closed and with tubular support. The latter result generalizes the case $p=n?1$ proved by M. Blel, S.K. Mimouni and G. Raby, which is also a generalization of the case when T is the current of integration on an hypersurface as proved by M.T. Togni. To cite this article: F. Elkhadhra, S.K. Mimouni, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Décompte dans une conjecture de Lang

Faltings has proven the following conjecture of Lang: if A is an abelian variety over a number field and X any subvariety then all rational points of X lie on a finite number N of translates, contained in X, of abelian subvarieties of A. We provide an upper bound for N whose main feature is uniformity in X since it does not depend on the height of X. Moreover, the bound is completely explicit. Together with the result of a previous paper, the heart of the proof is a suitable generalization of Mumford’s theorem for curves.

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Décompte dans une conjecture de Lang

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Oblatum 20-III-2000 & 3-V-2000?Published online: 16 August 2000     

Sur une propriété des nombres naturels

Résumé L'auteur donne des conditions nécessaires et suffisantes pour qu'un nombre naturel n soit un ? nombre pratique ?, c'est-à-dire pour que tout nombre naturel <-n soit une somme de diviseurs naturels distincts du nombre n. à Mauro Picone pour son 70^me anniversaire.     

L’Extension Abelienne D’une Categorie semi-abelienne

We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK ^x with the followings properties:

Moyennes uniformes et moyennes suivant une marche aléatoire

Summary Let be a bounded function on such that converges towards l as n goes to infinity, uniformly with respect to m. Let {X _n} be a random walk on , not concentrated on a proper subgroup of Then, with probability 1, converges towards l as n goes to infinity. The result also holds for any countable abelian group instead of . Other modes of convergence are considered (Cesaro convergence of order >1/2). The Cesaro convergence of expressions such that (X _n) (X _n+1) is also investigated.     

Sur une question d'Erdös et Schinzel,II

Sans résumé     

Sur une inégalité de F. Treves

Sans résuméA la mémoire deLeon Lichtenstein     

Sur deux congruences associées à une congruence W

Sans résuméEn l'honneur de M. E. Kruppa     

Invariants relatifs : une algèbre extérieure

Let G be a complex reflection group acting on V, M be a finite dimensional G-module and S be the coordinate ring of V. Generalizing results of Orlik and Solomon, and of Shepler, we build an exterior algebra structure on the set of relative invariants (associated to a linear character of G) of the algebra $S?\Lambda (M^1)$. To cite this article: V. Beck, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Compatibilité d'un fibré de Dirac avec une connexion

We extend to an almost Dirac structure and affine connections the notion of compatibility of a bivectors field or a 2-differential form with a pseudo-metric. Compatibility with a symmetric connection implies integrability. We shall be interested especially by such structures on Lie groups or Riemannian homogeneous spaces.