  In this paper, we prove that a complete Noetherian local domain of mixed
characteristic $p>0$ with perfect residue field has an integral extension that
is an integrally closed, almost Cohen-Macaulay domain such that the Frobenius
map is surjective modulo $p$. This result is seen as a mixed characteristic
analogue of the fact that the perfect closure of a complete local domain in
positive characteristic is almost Cohen-Macaulay. To this aim, we carry out a
detailed study of decompletion of perfectoid rings and establish the
Witt-perfect (decompleted) version of Andr\'e's perfectoid Abhyankar's lemma
and Riemann's extension theorem.
