A note on the Gauss–Manin connection for abelian schemes

We study differential forms on the universal vector extension A\ of an abelian scheme A in characteristic zero, and derive a new construction of the D-group scheme structure on A\. This gives, in particular, a rather simple description of the Gauss–Manin connection on the de Rham cohomology of A in terms of global algebraic differential forms on A\. The key ingredient is the computation of the coherent cohomology of A\, due to Coleman and Laumon.