Complete systems of addition laws on Abelian varieties.
Completely faithful Selmer groups over Kummer extensions.
Complex analytic geometry of complex parallelizable manifolds
Complex Subspaces of Homogeneous Complex Manifolds. I. Submanifolds of Abelian Varieties.
Component groups of abelian varieties and Grothendieck's duality conjecture
We investigate Grothendieck’s pairing on component groups of abelian varieties from the viewpoint of rigid uniformization theory. Under the assumption that the pairing is perfect, we show that the filtrations, as introduced by Lorenzini and in a more general way by Bosch and Xarles, are dual to each other. Furthermore, the methods yield some progress on the perfectness of the pairing itself, in particular, for abelian varieties with potentially multiplicative reduction.
Component groups of Néron models via rigid uniformization.
Computing the cardinality of CM elliptic curves using torsion points
Let be an elliptic curve having complex multiplication by a given quadratic order of an imaginary quadratic field . The field of definition of is the ring class field of the order. If the prime splits completely in , then we can reduce modulo one the factors of and get a curve defined over . The trace of the Frobenius of is known up to sign and we need a fast way to find this sign, in the context of the Elliptic Curve Primality Proving algorithm (ECPP). For this purpose, we propose...
Concavity Theorems.
Congruences between cusp forms and the geometry of Jacobians of modular curves.
Congruences entre séries d'Eisenstein, dans le cas supersingulier.
Congruences for Special Values of L-functions of Elliptic Curves with Complex Multiplication.
Conjugation of Kuga fiber varieties.
Connectedness results for -adic representations associated to abelian varieties
Construction analytique (rigide) de variétés abéliennes
Construction analytique rigide de variétés abéliennes
Corestriction of central simple algebras and families of Mumford-type
Let be a family of Mumford-type, that is, a family of polarized complex abelian fourfolds as introduced by Mumford in [9]. This family is defined starting from a quaternion algebra over a real cubic number field and imposing a condition to the corestriction of such . In this paper, under some extra conditions on the algebra , we make this condition explicit and in this way we are able to describe the polarization and the complex structures of the fibers. Then, we look at the non simple -fibers...
Correction and remarks concerning quasifunctions on elliptic curves.
Correction to “Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one”
Correspondances de Hecke, action de Galois et la conjecture d’André–Oort
Soient une variété de Shimura, fermée et irréductible et un ensemble Zariski dense de points spéciaux. Selon la conjecture d’André–Oort, est une sous-variété de type Hodge. Par exemple, si est un espace de modules de variétés abéliennes, est un ensemble de points correspondant à des variétés de type CM et doit paramétrer des variétés abéliennes munies de certaines classes de Hodge. En utilisant les actions de l’algèbre de Hecke et du groupe de Galois, Edixhoven et Yafaev montrent certains...
Corrigendum to Integral points on Abelian varieties.