Speaker: Rajat Kumar Mishra
Date: September 25, 2025
Affiliation: TIFR, Mumbai

Abstract: Let $K$ be a field of characteristic zero with a fixed derivation $\partial$ 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 $K(G)$ (also known as the Manin Kernel) is a finite dimensional $D$-group scheme that is a vectorial extension of such a general $G$. <br> <br> <br>