Automorphism groups of Ree type Deligne-Lusztig curves and function fields.
Automorphism groups of the modular curves
Belyi's theorem revisited.
Berichtigung zu der Arbeit: On Algebraic Curves over Real Closed Fields. Math. Z. 150, 49-70 (1976).
Bounds for the minimal solution of genus zero diophantine equations
Canonical integral structures on the de Rham cohomology of curves
For a smooth and proper curve over the fraction field of a discrete valuation ring , we explain (under very mild hypotheses) how to equip the de Rham cohomology with a canonical integral structure: i.e., an -lattice which is functorial in finite (generically étale) -morphisms of and which is preserved by the cup-product auto-duality on . Our construction of this lattice uses a certain class of normal proper models of and relative dualizing sheaves. We show that our lattice naturally...
Capacity theory on algebraic curves and canonical heights
Certain maximal curves and Cartier operators
Characteres and Galois invariants of regular dessins.
We describe a new invariant for the action of the absolute Galois groups on the set of Grothendieck dessins. It uses the fact that the automorphism groups of regular dessins are isomorphic to automorphism groups of the corresponding Riemman surfaces and define linear represenatations of the space of holomorphic differentials. The characters of these representations give more precise information about the action of the Galois group than all previously known invariants, as it is shown by a series...
Class numbers of quadratic fields and Shimura's correspondence.
Classes d'idéaux et classes de diviseurs
Cohomologie des courbes elliptiques
Combinatoire des arbres planaires et arithmétique des courbes hyperelliptiques
Le but de cet article est de proposer une nouvelle méthode pour des études dans le cadre de la théorie des “dessins d’enfants” de A. Grothendieck de certaines questions concernant l’action du groupe de Galois absolu sur l’ensemble des arbres planaires.On définit l’application qui associe à chaque arbre planaire à arêtes, une courbe hyperelliptique avec un point de -division. Cette construction permet d’établir un lien entre la théorie de la torsion des courbes hyperelliptiques et celle des “dessins...
Combinatorica delle T-curve separanti
Complete arcs arising from a generalization of the Hermitian curve
We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin-Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.
Congruences for Special Values of L-functions of Elliptic Curves with Complex Multiplication.
Construction analytique de courbes en géométrie non archimédienne
Counting points on curves over finite fields
Coupling of universal monodromy representations of Galois-Teichmüller modular groups.
Courbes de Shimura hyperelliptiques