Affine Parts of Abelian Surfaces as Complete Intersections of Four Quadrics.
Alcôves et -rang des variétés abéliennes
On étudie la relation entre le -rang des variétés abéliennes en caractéristique et la stratification de Kottwitz-Rapoport de la fibre spéciale en de l’espace de module des variétés abéliennes principalement polarisées avec structure de niveau de type Iwahori en . En particulier, on démontre la densité du lieu ordinaire dans cette fibre spéciale.
Algebraic cycles in families of abelian varieties over Hilbert-Blumenthal surfaces.
Algebraic cycles on abelian varieties and their decomposition
For an Abelian Variety , the Künneth decomposition of the rational equivalence class of the diagonal gives rise to explicit formulas for the projectors associated to Beauville's decomposition (1) of the Chow ring , in terms of push-forward and pull-back of -multiplication. We obtain a few simplifications of such formulas, see theorem (4) below, and some related results, see proposition (9) below.
Algebraic Cycles on Abelian Varieties of Fermat Type.
Algebraic cycles on generic abelian varieties
Algebraic groups associated with abelian varieties.
Algebraic methods in the theory of theta functions
Algebraic points of abelian functions in two variables
Algebraically completely integrable systems and Kummer varieties.
An analytic construction of degenerating abelian varieties over complete rings
An arithmetic of modular function fields of degree two
An explicit formula for period determinant
We consider a generic complex polynomial in two variables and a basis in the first homology group of a nonsingular level curve. We take an arbitrary tuple of homogeneous polynomial 1-forms of appropriate degrees so that their integrals over the basic cycles form a square matrix (of multivalued analytic functions of the level value). We give an explicit formula for the determinant of this matrix.
An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
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.
Andreotti-Mayer loci and the Schottky problem.
Annexe: Deux lettres
Approximation diophantienne sur les variétés semi-abéliennes
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.