  In differential algebra, a proper scheme $X$ defined over an algebraically
closed field $K$ with a derivation $\partial$ on it descends to the field of
constants $K^\partial$ if $X$ itself lifts the derivation $\partial$. This is a
result by A. Buium. Now in the arithmetic case, the notion of a derivation is
replaced by the notion of a $\pi$-derivation $\delta$ or equivalently in the
flat case, a lift of Frobenius $\phi$. We will show an analogous result in the
arithmetic case of equal characteristic. We show our results using the
arithmetic analogue of Taylor expansion using Witt vectors.
