An Example of Unirational Surfaces in Characteristic p.
An explicit algebraic family of genus-one curves violating the Hasse principle
We prove that for any , the curvein is a genus curve violating the Hasse principle. An explicit Weierstrass model for its jacobian is given. The Shafarevich-Tate group of each contains a subgroup isomorphic to .
An explicit factorisation of the zeta functions of Dwork hypersurfaces
An explicit version of Birch's Theorem
An injective rational map of an abstract algebraic variety into itself.
An iterative construction for ordinary and very special hyperelliptic curves
Si costruiscono famiglie di curve iperellittiche col —rango della varietà jacobiana uguale a zero. La costruzione sfrutta le proprietà elementari dell’operatore di Cartier e delle estensioni -cicliche dei corpi con la caratteristica maggiore di zero.
Analytic cell decomposition and analytic motivic integration
Analytic functions on an open subsets of P1 (k).
Analytic Lifting of Algebraic Tori.
Another Look at p-Adic L-Functions for Totally Real Fields.
Appendice: Sur un théorème de Bloch et Kato (lettre à B. Perrin-Riou).
Applications de la théorie de Kummer à des problèmes de transcendance.
Approximation diophantienne dans les groupes algébriques commutatifs. (I): Une version effective du théorème du sous-group algébrique.
Approximation faible aux places de bonne réduction sur les surfaces cubiques sur les corps de fonctions
On démontre que les surfaces cubiques lisses sur les corps de fonctions d’une courbe sur un corps algébriquement clos de caractéristique vérifient l’approximation faible aux places de bonne réduction. La méthode utilisée imite celle employée par Swinnerton-Dyer [10] dans le cas des corps de nombres.
Approximations diophantiennes -adiques sur les courbes elliptiques admettant une multiplication complexe
Arakelov Chow groups of abelian schemes, arithmetic Fourier transform, and analogues of the standard conjectures of Lefschetz type.
Arakelov computations in genus curves
Arakelov invariants of arithmetic surfaces are well known for genus 1 and 2 ([4], [2]). In this note, we study the modular height and the Arakelov self-intersection for a family of curves of genus 3 with many automorphisms:Arakelov calculus involves both analytic and arithmetic computations. We express the periods of the curve in terms of elliptic integrals. The substitutions used in these integrals provide a splitting of the jacobian of as a product of three elliptic curves. Using the corresponding...
Arakelov invariants of Riemann surfaces.
Arakelov's Theorem for Abelian Varieties.
Arithmetic and geometry of the curve y³+1=x⁴