De Rham-Witt cohomology and displays

Abstract

Displays were introduced to classify formal $p$-divisible groups over an arbitrary ring $R$ where $p$ is nilpotent. We define a more general notion of display and obtain an exact tensor category. In many examples the crystalline cohomology of a smooth and proper scheme $X$ over $R$ carries a natural display structure. It is constructed from the relative de Rham-Witt complex. For this we refine the comparison between crystalline cohomology and de Rham-Witt cohomology of [LZ]. In the case where $R$ is reduced the display structure is related to the strong divisibility condition of Fontaine [Fo].