On the extensions of $\acute{W}_{n}$ by $\mathscr{G}_{(\mu)}$ over a $Z_{(p)}$-algebra

Abstract

We will give an explicit description of extensions of the group scheme of Witt vectors of length $n$ (resp. the formal group scheme of Witt vectotrs of length $n$) by the group scheme (resp. the formal group scheme) which gives a deformation of the additive group scheme to the multiplicative group scheme (resp. the additive formal group scheme to the multiplicative formal group scheme) over an algebra for which all prime numbers except a given prime $p$ are invertible.