Triades et familles de courbes gauches

Construction De Familles Minimales De Courbes Gauches

Let A be a noetherian local ring, and let C in PA be a family of curves, flat over A. We showed in an earlier paper how to associate to C a locally free sheaf N on PA, and we showed that two families of curves C,C′ are in the same biliaison class if and only if the corresponding sheaves N,N ′ are pseudoisomorphic (generalization of the theorem Rao). In this paper we show how to find all the fla...

Familles de graphes de présentation finie, propriétés et applications

Families of Hyperelliptic Curves with Real Multiplication Familles de courbes hyperelliptiques à multiplications réelles

where bxc denotes the integer part of x. We say that a curve C of genus bn/2c, defined over a field k, has real multiplication by Gn if there exists a correspondence C on C such that Gn is the characteristic polynomial of the endomorphism induced by C on the regular differentials on C . The endomorphism ring of the Jacobian JC of such a curve C contains a subring isomorphic to Z[X ]/(Gn(X )) wh...

Courbes modulaires et 11-rang de corps quadratiques

TABLE DES MATI`ERES Introduction 1. Structure galoisienne de courbes modulaires 2. Le cas p = 23 3. Méthode et Résultats Remerciements Bibliographie Nous construisons 53 corps quadratiques imaginaires ayant un 11-rangégaì a 3, et sept corps quadratiques réels de 11-rangégaì a 2. Ce sont, ` a notre connaissance, les premiers exemples de tels corps. We construct 53 imaginary quadratic fields of 1...

Courbes hyperelliptiques à multiplications réelles et une construction de Shih

Let r and p be distinct prime numbers, let K = Q(cos 2π r ), and let F be the residue field of K at a place above p. When the image of (2 − 2 cos 2π r ) in F is not a square, we describe a geometric construction of a regular extension of K(t) with Galois group PSL2(F). This extension corresponds to a covering of P/K of “signature (r, p, p)” in the sense of [3, sec. 6.3], and its existence is pr...