Hi. I don't know how to make a comment; this is on Torsten's example with elliptic curve minus zero point. When you take a line bundle corresponding to a point (not a two torsion point) and add the line bundle corresponding to minus of that point then this rang=2 vector bundle restricted to the elliptic curve minus zero is  (even globally) free.

Indeed, working on the elliptic curve twist with the degree one line bundle L corresponding to the zero point and take the canonical inclusion of the structure sheaf on both factors, the quotient must be isomorphic to L squared.

This is just to understand Bass' theorem on this nice example. I don't really understand what happens with the two torsion points.

Hi. I don't know how to make a comment; this is on Torsten's example with elliptic curve minus zero point. When you take a line bundle corresponding to a point (for simplicity not a two torsion point) and add the line bundle corresponding to minus of that point then this rank=2 vector bundle restricted to the elliptic curve minus zero is  (even globally) free.

Indeed, working on the elliptic curve twist with the degree one line bundle L corresponding to the zero point and take the canonical inclusion of the structure sheaf on both factors, the quotient must be isomorphic to L squared.

This is just to understand Bass' theorem on this nice example.