P-adic Superspaces and Frobenius

The notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over Z p (the ring of p-adic integers). This article partially intersects with [9]; it contains the proofs omitted in [9] as well as some investigations into the important notion of a prorepresentable p-adic superspace.