Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication.
The analytic order of III for modular elliptic curves
In this note we extend the computations described in [4] by computing the analytic order of the Tate-Shafarevich group III for all the curves in each isogeny class ; in [4] we considered the strong Weil curve only. While no new methods are involved here, the results have some interesting features suggesting ways in which strong Weil curves may be distinguished from other curves in their isogeny class.
The Arithmetic of Elliptic Curves.
The average rank of elliptic curves I. With Appendix "The Explicit formula for elliptic curves over function fields" by Oisín McGuinness.
The canonical height and integral points on elliptic curves.
The dimension of the derived category of elliptic curves and tubular weighted projective lines
We show that the dimension of the derived category of an elliptic curve or a tubular weighted projective line is one. We give explicit generators realizing this number, and show that they are in a certain sense minimal.
The equation xyz = x + y + z = 1 in integers of a cubic field.
The field of definition of the Mordell-Weil group of an elliptic curve over a function field
The Group of Automorphisms of the Modular Function Field.
The moduli space of curves of genus two covering elliptic curves.
The number of elliptic curves over Q with conductor N.
The optimality of the Bounded Height Conjecture
In this article we show that the Bounded Height Conjecture is optimal in the sense that, if is an irreducible subvariety with empty deprived set in a power of an elliptic curve, then every open subset of does not have bounded height. The Bounded Height Conjecture is known to hold. We also present some examples and remarks.
The -adic gamma function and the congruences of Atkin and Swinnerton-Dyer
The scheme of morphisms from an elliptic curve to a Grassmannian
The subbundles of decomposable vector bundles over on elliptic curve.
Let C be an elliptic curve and E, F polystable vector bundles on C such that no two among the indecomposable factors of E + F are isomorphic. Here we give a complete classification of such pairs (E,F) such that E is a subbundle of F.
The tautological ring of
We describe the tautological ring of the moduli space of stable -pointed curves of genus one of compact type. It is proven that it is a Gorenstein algebra.
The torsion subgroup of a family of elliptic curves over the maximal abelian extension of
We determine explicitly the structure of the torsion group over the maximal abelian extension of and over the maximal -cyclotomic extensions of for the family of rational elliptic curves given by , where is an integer.
The underlying real algebraic structure of complex elliptic curves.
The Witt ring of an elliptic curve over a local field.
Théorie d'Iwasawa p-adique locale et globale.