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).