GLOBAL WEIERSTRASS EQUATIONS OF HYPERELLIPTIC CURVES
Résumé
Given a hyperelliptic curve C of genus g over a number field K and a Weierstrass model {\mathsrc C} of C over the ring of integers O_K (i.e. the hyperelliptic involution of C extends to {\mathsrc C} and the quotient is a smooth model of P1_K over OK), we give necessary and sometimes sufficient conditions for {\mathsrc C} to be defined by a global Weierstrass equation. In particular, if C has everywhere good reduction, we prove that it is defined by a global Weierstrass equation with invertible discriminant if the class number hK is prime to 2(2g+1), confirming a conjecture of M. Sadek.
Origine | Fichiers produits par l'(les) auteur(s) |
---|