Calcul des résidus en analyse -adique
Canonical heights on varieties with morphisms
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...
Certain maximal curves and Cartier operators
Character sums in finite fields
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...
Characteristic Classes of Kuga Fiber Varieties of Quaternion Type.
Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation
We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a “rigidity” approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characters to Grothendieck-Teichmüller groups.
Chern classes, adeles and L-functions.
Chern numbers of cusp resolutions in totally real cubic number fields.
Chern numbers of Hilbert modular varieties.
Class numbers of quadratic fields and Shimura's correspondence.
Classe de conjugaison du frobenius des variétés abéliennes à réduction ordinaire
Soient une variété abélienne sur un corps de nombres et son groupe de Mumford–Tate. Soit une valuation de et pour tout nombre premier tel que , soit l’automorphisme de Frobenius (géométrique) de la cohomologie étale -adique de . On montre que si a une bonne réduction ordinaire en , alors il existe tel que, pour tout , soit conjugué à dans . On montre un résultat analogue pour le frobenius de la cohomologie cristalline de la réduction de modulo .
Classes de Chern et classes de cycles en cohomologie rigide
Nous construisons dans cet article les classes de Chern et les classes de cycles en cohomologie rigide. Nous démontrons par la suite que ces constructions vérifient bien les propriétés attendues. La cohomologie rigide est donc une cohomologie de Weil.
Classical and overconvergent modular forms
Classical Godeaux Surface in Characteristic P.
Classification of non-rigid families of K3 surfaces and a finiteness theorem of Arakelov type.
Classification of projective surfaces with small sectional genus : char >
CM points and quaternion algebras.
Co-fibered products of algebraic curves
We give examples of failure of the existence of co-fibered products in the category of algebraic curves.