A basis for the non-archimedean holomorphic theta functions.
A generalization of the Chowla-Selberg formula.
Abelian surfaces and products of elliptic curves
Si dà una nuova e completa dimostrazione del risultato cruciale del metodo di Ruppert che consente di stabilire in maniera effettiva quando una superficie abeliana è isomorfa o isogena a un prodotto di curve ellittiche.
Abelian varieties over fields of finite characteristic
The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.
Bounds on polarizations of abelian varieties over finite fields.
Classes d'isogénie des variétés abéliennes sur un corps fini
Congruences between cusp forms and the geometry of Jacobians of modular curves.
Decompositions of an Abelian surface and quadratic forms
When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.
Descent via isogeny in dimension 2
Endomorphism estimates for abelian varieties.
Estimating isogenies on elliptic curves.
Factorization estimates for abelian varieties
Galois descent and twists of an abelian variety
La filtration canonique des points de torsion des groupes -divisibles
Étant donnés un entier et un groupe de Barsotti-Tate tronqué d’échelon et de dimension sur un anneau de valuation d’inégales caractéristiques, nous donnons une borne explicite sur son invariant de Hasse qui implique que sa filtration de Harder-Narasimhan possède un sous-groupe libre de rang . Lorsque nous redémontrons également le théorème d’Abbes-Mokrane ([120]) et de Tian ([164]) par des méthodes locales. On applique cela aux familles -adiques de tels objets et en particulier à certaines...
L'opération de Cartier. Applications
Minorations de formes linéaires de logarithmes elliptiques
Motivic decomposition of abelian schemes and the Fourier transform.
On a theorem of Tate
We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.
On coverings of simple abelian varieties
To any finite covering of degree between smooth complex projective manifolds, one associates a vector bundle of rank on whose total space contains . It is known that is ample when is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when is a simple abelian variety and does not factor through any nontrivial isogeny . This result is obtained by showing that is -regular in the...
Optimal curves differing by a 3-isogeny
Stein and Watkins conjectured that for a certain family of elliptic curves E, the X₀(N)-optimal curve and the X₁(N)-optimal curve of the isogeny class 𝓒 containing E of conductor N differ by a 3-isogeny. In this paper, we show that this conjecture is true.