Complément à l'article de P. Deligne "La conjecture de Weil pour les surfaces K3".
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.
Comptage de courbes sur le plan projectif éclaté en trois points alignés
Nous établissons une version de la conjecture de Manin pour le plan projectif éclaté en trois points alignés, le corps de base étant un corps global de caractéristique positive.
Computation of L-series for elliptic curves over function fields.
Computing Igusa's local zeta functions of univariate polynomials, and linear feedback shift registers.
Computing special values of motivic -functions.
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...
Computing the characteristic polynomials of a class of hyperelliptic curves for cryptographic applications.
Congruence properties of the hyperkloosterman sum
Congruences between cusp forms and the geometry of Jacobians of modular curves.
Congruences et formes modulaires
Congruences for Special Values of L-functions of Elliptic Curves with Complex Multiplication.
Congruences of Cusp Forms and Special Values of Their Zeta Functions.
Congruenze per integrali ellittici
Conics in characteristic 2
Conjecture de Bloch et nombres de Milnor
Nous déduisons de la formule du conducteur, conjecturée par S. Bloch, celle de P. Deligne exprimant, dans le cas d'une singularité isolée, la dimension totale des cycles évanescents en fonction du nombre de Milnor. En particulier, la formule de Deligne est établie en dimension relative un; en appendice, on généralise cet énoncé au cas d'un lieu singulier propre.
Conjecture de Franchetta forte.
Conjugation of Kuga fiber varieties.
Construction analytique de courbes en géométrie non archimédienne