Valuation rings of mixed characteristic as limits of complete intersection rings

Abstract

We show that a mixed characteristic valuation ring with a value group $\Gamma$, $\val$ its valuation and a residue field of characteristic $p>0$, is a filtered colimit of complete intersection $\bf Z$-algebras if $\Gamma/{\bf Z}\val(p)$ has no $p$-torsion and $V$ is Henselian.