Rang de courbes elliptiques liees a certaines extensions cycliques de degre 4 et 6
Rational Bézier curves with infinitely many integral points
In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.
Rational points of a curve which has a nontrivial automorphism
Rational points on elliptic curves over Q in elementary abelian 2-extensions of Q.
Real algebraic curves
Real commutative algebra (II). Plane curves.
Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.
The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings of S which might...
Reciprocity laws on curves
Reed-Muller codes and supersingular curves. I
Revêtements étales d'une courbe de Mumford