Some estimates from étale cohomology.
Some examples of 5 and 7 descent for elliptic curves over
We perform descent calculations for the families of elliptic curves over with a rational point of order or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and 7, and show that the 5-torsion of the Tate-Shafarevich group of an elliptic curve over may become arbitrarily large.
Some families of non-congruent numbers
Some functions related to the derivatives of the L-series of an elliptic curve at s=1
Some new directions in -adic Hodge theory
We recall some basic constructions from -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of -pairs, introduced recently by Berger, which provides a natural enlargement of the category of -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology, including Tate...
Some observations on motivic cohomolgy of arithmetic schemes.
Some p-adic Galois Representations for Curves in Characteristic p.
Some remarks on plane curves over fields of finite characteristic
Some remarks on the arithmetic Hodge index conjecture
Some Results on the Mordell-Weil Group of the Jacobian of the Fermat Curve.
Some simple elliptic surfaces of genus zero.
Some special curves of genus 5
Sous-groupes à plusieurs paramètres -adiques de variétés abéliennes
Special values of -functions attached to
Spécialisation des revêtements en caractéristique
Specialization of the -adic polylogarithm to -th power roots of unity.
Spherical roots of spherical varieties
Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.
Stability of Arakelov bundles and tensor products without global sections.
Stable maps of curves.
Stable reduction and rigid analytic uniformization of abelian varieties