WITT VECTORS WITH p-ADIC COEFFICIENTS AND FONTAINE’S RINGS

We describe an alternate construction of some of the basic rings introduced by Fontaine in p-adic Hodge theory. In our construction, the central role is played by the ring of p-typical Witt vectors over a p-adic valuation ring, rather than theWitt vectors over a ring of positive characteristic. This suggests the possibility of forming a meaningful global analogue of p-adic Hodge theory.