Reed-Muller codes and supersingular curves. I
Reelle algebraische Funktionen mit vorgegebenen Null- und Polstellen.
Représentations galoisiennes associées aux points d’ordre des jacobiennes de certaines courbes de genre 2
Representations of integers by binary forms and the rank of the Mordell-Weil group.
R-equivalence and rationality problem for semisimple adjoint classical algebraic groups
-integral solutions to a Weierstrass equation
The rational solutions with as denominators powers of to the elliptic diophantine equation are determined. An idea of Yuri Bilu is applied, which avoids Thue and Thue-Mahler equations, and deduces four-term (-) unit equations with special properties, that are solved by linear forms in real and -adic logarithms.
Semialgebraic Topology Over a Real Closed Field I: Paths and Components in the Set of Rational Points of an Algebraic Variety.
Semialgebraic Topology over a Real Closed Field II: Basic Theory of Semialgebraic Spaces.
Sequences of rational torsions on abelian varieties.
Séries d'Eisenstein et fonctions L de courbes elliptiques à multiplication complexe.
Severi`s Conjecture on 0-Cycles for a Complete Intersection.
S-ganze Punkte auf elliptischen Kurven.
Simultaneous resolution of rational singularities
Solving an indeterminate third degree equation in rational numbers. Sylvester and Lucas
This article concerns the problem of solving diophantine equations in rational numbers. It traces the way in which the 19th century broke from the centuries-old tradition of the purely algebraic treatment of this problem. Special attention is paid to Sylvester’s work “On Certain Ternary Cubic-Form Equations” (1879–1880), in which the algebraico-geometrical approach was applied to the study of an indeterminate equation of third degree.
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 Results on the Mordell-Weil Group of the Jacobian of the Fermat Curve.
Some simple elliptic surfaces of genus zero.