Logarithmic derivatives of Dirichlet -functions and the periods of abelian varieties
Loi de réciprocité quadratique dans les corps quadratiques imaginaires
À partir d’une courbe elliptique définie sur le corps des classes de Hilbert d’un corps quadratique imaginaire et à multiplicité complexe par l’anneau des entiers de , on construit des fonctions elliptiques. Nous établissons des formules produits relatives à ces fonctions. De ce fait, nous obtenons une formulation analytique du lemme de Gauss généralisé ainsi qu’une expression explicite pour le symbole quadratique de Legendre défini sur l’anneau des entiers du corps quadratique imaginaire. Comme...
Lois de réciprocité liées aux courbes elliptiques
Lokal-Global-Prinzipien für die Brauergruppe.
Loop groups, elliptic singularities and principal bundles over elliptic curves
There is a well known relation between simple algebraic groups and simple singularities, cf. [5], [28]. The simple singularities appear as the generic singularity in codimension two of the unipotent variety of simple algebraic groups. Furthermore, the semi-universal deformation and the simultaneous resolution of the singularity can be constructed in terms of the algebraic group. The aim of these notes is to extend this kind of relation to loop groups and simple elliptic singularities. It is the...
Lower Bounds for Heights on Elliptic Curves.
Lower bounds on the class number of algebraic function fields defined over any finite field
We give lower bounds on the number of effective divisors of degree with respect to the number of places of certain degrees of an algebraic function field of genus defined over a finite field. We deduce lower bounds for the class number which improve the Lachaud - Martin-Deschamps bounds and asymptotically reaches the Tsfasman-Vladut bounds. We give examples of towers of algebraic function fields having a large class number.
L'unirazionalità della varietà dei moduli delle curve di genere dodici
Matching local Witt invariants
The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.
Maximal rank curves and singular points of the Hilbert scheme
Maximal Subbundles of Rank Two Vector Bundles on Curves.
Maximal Subbundles of Vector Bundles on a Curve.
Meromorphe Funktionen auf Mumfords Kompaktifizierung der universellen elliptischen Kurve N-ter Stufe.
Minimal models for elliptic curves with complex multiplication
Minimal resolution and stable reduction of
Let be an integer. Let be the modular curve over , as constructed by Katz and Mazur. The minimal resolution of over is computed. Let be a prime, such that , with prime to . Let . It is shown that has stable reduction at over , and the fibre at of the stable model is computed.
Minimal sets of generators for the relation ideals of certain monomial curves.
Minimalité des courbes sous-canoniques
Soient un fibré de rang 2 sur l’espace projectif de dimension 3 sur un corps algébriquement clos et un entier tel que et . Toute courbe schéma des zéros d’une section non nulle de est une courbe minimale dans sa classe de biliaison.
Minorant de la dérivée au point de la fonction attachée à une courbe elliptique de Weil
Mirror symmetry and toric geometry.
Modèles minimaux des courbes de genre deux.