Contenu
Points algébriques de degré au plus 4 sur la courbe
d’équation affine y2 = x(x - 3)(x - 4)(x - 6)(x - 7)
Boubacar Sidy BALDE (1) and Oumar SALL (2)
Laboratoire: Mathématiques et Applications (LMA),
U.F.R des Sciences et Technologies,
Université Assane Seck de Ziguinchor,
BP 523 Ziguinchor Sénégal
Mathematics Subject Classification: (2010) 14H50, 14H40, 11D68
Key words: Mordell-Weil Group. Jacobian. Galois Conjugates. Algebraic
extensions. The Abel-Jacobi theorem. Linear systems.
Abstract:
In this work, we use the finiteness of the Mordell-weil group of the
Jacobian variety of and the Riemann Roch spaces to determine the set
of algebraic points of degree at most four over ℚ on the affine curve
: y2 = x(x - 3)(x - 4)(x - 6)(x - 7).
The results obtained extend the work of Daniel M.Gordon and David Grant in
[1], who determined the Mordell-Weil group J(ℚ) and the set of rational points
on the same curve.