Differential Characters and D-Group Schemes

Let K be a field of characteristic zero with a fixed derivation ∂ on it. In the case when A is an abelian scheme, Buium considered the group scheme K(A) which is the kernel of differential characters (also known as Manin characters) on the jet space of A. Then K(A) naturally inherits a D-group scheme structure. Using the theory of universal vectorial extensions of A, he further showed that K(A) is a finite dimensional vectorial extension of A. Let G be a smooth connected commutative finite dimensional group scheme over Spec K. In this paper, using the theory of differential characters, we show that the associated kernel group scheme K(G) is a finite dimensional D-group scheme that is a vectorial extension of such a general G. Our proof relies entirely on understanding the structure of jet spaces. Our method also allows us to give a classification of the module of differential characters X<inf>∞</inf>(G) in terms of primitive characters as a K{∂}-module.