 If the base "X" is a complex manifold, then an invertible sheaf is (the sheaf of sections of) a holomorphic line bundle, and trivial means holomorphically equivalent to a trivial bundle, not just topologically equivalent.Weil's result has been restated in terms of biextensions, a concept now generally used in the duality theory of abelian varieties.The theorem of the square is a corollary (also due to Weil) applying to an abelian variety "A".