Speaker: Rajat Kumar Mishra
Venue: TIFR, Mumbai
Date: September 9, 2025

Differential Characters and The Manin Kernel: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 \Spec𝐾 . 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 .