Groupes fondamentaux motiviques de Tate mixte

We define the category of mixed Tate motives over the ring of S-integers of a number field. We define the motivic fundamental group (made unipotent) of a unirational variety over a number field. We apply this to the study of the motivic fundamental group of the projective line punctured at zero, infinity and all Nth roots of unity.     

Groupes vectoriels et schéma de Picard

This Note contains slight variations on a well known theme: linear sub-groups of the Picard functor of a proper scheme over a field k. In particular, we give exemples of a field k, with positive characteristic, and a projective k-scheme X, normal, but not geometrically reduced, such that the neutral component of its Picard functor is representable by a nonzero vectorial group scheme. To cite this article: M. Raynaud, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Groupes libres et algebses de groupes en geometrie algebrique

Let X=Sp A be an affine scheme over a perfect field k of positive caracteristic. The functor D(k)-mod (W(A), (w(?)) is the unipotent part of the affine commutative free group generated by X (W is the ring of Witt-vectors and D the ring of Dieudonné). If X is a monoïd-scheme, this free group has a structure of ring scheme. In particular, if X=0 _k ^x , we obtain a new proof of the theorem of decomposition of the universal ring.     

Groupes de Lubin-Tate généralisés

Sans résuméA Jean-Pierre Serre, en témoignage de 25 ans d'amitié et d'échanges confiantsDirecteur de Recherches au Centre National de la Recherche Scientifique. L'auteur remercie cette institution pour le soutien financier qu'elle lui fournit     

Groupes de permutations primitifs d'ordre impair et denombrement de tournois sommet-primitifs

A tournament T (directed graph in which there is exactly one arc between any two vertices) is said to be point-primitive if its automorphism group A(T) acts primitively on the vertices of T. Automorphism groups of point-primitive tournaments are primitive permutation groups of odd order, which are known to be affine groups; and so point-primitive tournaments are of prime-power order. Some properties of primitive permutation groups of odd order are proved and a counting formula for point-primitive tournaments of order p^2k (p prime number, k integer ?0) is derived from them.     

Groupes de cohomologie d'un fibré holomorphe à base et à fibre de Stein

Sans résumé     

Le Nombre D’images Homomorphes de Certains Groupes et Algèbres de Golod

We investigate homomorphic images of Golod algebras. We prove that some quotients of certain Golod algebras are Golod algebras too. We determine classes of Golod algebras and nilalgebras not satisfying Golod properties which have a continuum of non isomorphic homomorphic images. We establish analogous results for Lie algebras and p-groups of Golod type.     

Groupes de type [d→3(d−1)]

Sans résumé     

Groupes de Chow etK-théorie de variétés sur un corps fini

Sans résumé     

Groupes d’homotopie des variétés de Stiefel complexes

Sans résumé L’auteur tient à remercier vivement MM. les professeursB. Eckmann etP. J. Hilton pour leurs suggestions enrichissantes au cours de la rédaction de ce travail.