| Consider an integral and normal, complex quasi-projective variety Y with a projective morphism to a Dedekind scheme S. Let L be a non-trivial line bundle on Y, such that for all curves C→sY , finite over S, the pull-back sigma* L is trivial. The following discussion will show that L must be a torsion bundle when S is a complex affine normal curve. Furthermore, it will be seen that the result is independent of the fibration over S, so long as Y has a smooth compactification. |
