Displays and gauges

We introduce the notion of an F-gauge and show, how these objects are connected to F-zips and displays. After establishing these relationships, we define the syntomic sheaves Oncris and prove, that these sheaves are flat over the truncated ring of Witt vectors W_n with coefficients in a perfect field of positive characteristic. This enables us to define a sheaf of rings on the small syntomic site of a perfect field in characteristic p>0. This sheaf was first introduced by Jean-Marc Fontaine and Uwe Jannsen to establish a new p-adic cohomology theory. We proof some elementary facts about this sheaf. Also the notion of phi-gauges is defined and we clarify, how it is related to F-gauges.