On the problem of detecting linear dependence for products of abelian varieties and tori
On the Rational Points of Abelian Varieties over Zp Extensions of Number Fields.
On the Real Points of an Arithmetic Quotient of a Bounded Symmetrie Domain.
On the reduction of abelian varieties
On the reduction of the Hilbert-Blumenthal-moduli scheme with ...(p)-level structure.
On the Shafarevich and Tate conjectures for hyperkähler varieties.
On the Shafarevich-Tate group of the jacobian of a quotient of the Fermat curvature.
On the strange duality conjecture for abelian surfaces
We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.
On the Structure of the Birational Abel Morphism.
On the tautological ring of Mg.
On theta functions with complex multiplication.
On translation invariance for Wrd.
One attempt to the modular function - II
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.
Optimal curves differing by a 5-isogeny
For i = 0,1, let be the -optimal curve of an isogeny class of elliptic curves defined over ℚ of conductor N. Stein and Watkins conjectured that E₀ and E₁ differ by a 5-isogeny if and only if E₀ = X₀(11) and E₁ = X₁(11). In this paper, we show that this conjecture is true if N is square-free and is not divisible by 5. On the other hand, Hadano conjectured that for an elliptic curve E defined over ℚ with a rational point P of order 5, the 5-isogenous curve E’ := E/⟨P⟩ has a rational point of order...
Ordinariness in good reductions of Shimura varieties of PEL-type
Origine géométrique et représentation géométrique des fonctions elliptiques, abéliennes et de transcendantes d'ordres supérieurs.
-adic heights for semi-stable abelian varieties
-adic -functions for elliptic curves with complex multiplication I
-adic representations arising from descent on abelian varieties