Weak Hasse Principle for Cubic Forms

Ivica Gusić, Zagreb, Croatia

Keywords: p-adic field, quadratic form, equivalence of quadratic forms, cubic form, algebraic curve, morphism, unramified morphism, k-rational point, elliptic curve, isogeny, good reduction AMS Subject classification: 11E99, 11G05, 14G99

Abstract: It is shown that the Faltings Theorem on isogenies of elliptic curves is a natural generalization of the Weak Hasse Principle on ternary quadratic forms.