We establish a formula for homomorphisms and extensions of group schemes and formal groups, related to deformations of the multiplicative group to the additive group. As an application, we give an explicit description of the theory unifying the Kummer and Artin-Schreier-Witt theories of degree $p^2$.
"A note on extensions of algebraic and formal groups, IV. Kummer-Artin-Schreier-Witt theory of degree $p^2$." Tohoku Math. J. (2) 53 (2) 203 - 240, 2001. https://doi.org/10.2748/tmj/1178207479