In 'The universal vectorial Bi-extension and p-adic heights' Coleman works with the pullback of the Poincaré biextension of an abelian variety A to its universal vectorial extension and claims this is a scheme and I would like to know how to see that this is in fact a scheme. I understand that biextensions of abelian varieties are torsors in a sheaf-theoreic way and I know from Milne's remark on his étale cohomology book that torsors in this way can correspond to schemes ( through usual representability, I assume ) but in this particular case I can't seem to be able to show this. Any reference would be greatly appreciated.