Fontaine rings and local cohomology

We use a construction due to Fontaine to construct rings with almost vanishing local cohomology from rings of mixed characteristic and discuss the question of using this method to construct almost Cohen–Macaulay algebras over the original ring. We also show that the existence of almost Cohen–Macaulay algebras implies the Monomial Conjecture and give an example to show how this procedure can be carried out in a nontrivial case.