À propos de la conjecture de Manin pour les courbes elliptiques modulaires
À propos de la forme hermitienne canonique d'une singularité isolée d'hypersurface
À propos du théorème de Belyi
Le théorème de Belyi affirme que sur toute courbe algébrique lisse projective et géométriquement connexe, définie sur , il existe une fonction non ramifiée en dehors de . Nous montrons que cette fonction peut être choisie sans automorphismes, c’est-à-dire telle que pour tout automorphisme non trivial de , on ait . Nous en déduisons que si est une extension finie de , toute -classe d’isomorphisme de courbes algébriques lisses projectives géométriquement connexes peut être caractérisée...
A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.
A really elementary proof of real Lüroth's theorem.
Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K is a subfield...
A refined cojecture of Mazur-Tate type for Heegner points.
A remark about isogenies of elliptic curves over quadratic fields
A remark on a conjecture of Hain and Looijenga
We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all and if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.
A remark on a theorem of Chowla-Cowles.
A remark on Abel's Theorem and the mapping of linear series.
A remark on Abhyankar's space lines
A remark on Hodge cycles on moduli spaces of rank 2 bundles over curves.
A remark on the embedding theorem for general smooth curves.
A Remark on the Hilbert Scheme of smooth complex space curves.
A remark on the homotopical dimension of some moduli spaces of stable Riemann surfaces
Using a result of Harer, we prove certain upper bounds for the homotopical/cohomological dimension of the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most k rational components. These bounds would follow from conjectures of Looijenga and Roth–Vakil.
A remark on the paper of A. Tannenbaum
A remark on the Picard group of spin moduli space
We describe a number of classes in the Picard group of spin moduli space and determine the relations they satisfy; as an application we show that the Picard group in question contains 4-torsion elements.
A remark on the rational cohomology of .
A Remark on the Sato-Tate Conjecture.
A Riemann-Hurwitz formula for the Selmer group of an elliptic curve with complex multiplication.