De Rham-Witt cohomology and displays
Andreas LangerMathematics Fakultät für Mathematik University of Exeter Universität Bielefeld Exeter, EX4 4QE Postfach 100131 Devon, UK D-33501 Bielefeld
Thomas ZinkMathematics Fakultät für Mathematik University of Exeter Universität Bielefeld Exeter, EX4 4QE Postfach 100131 Devon, UK D-33501 Bielefeld
Displays were introduced to classify formal -divisible groups over an arbitrary ring where 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 over 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 is reduced the display structure is related to the strong divisibility condition of Fontaine [Fo].
Cite this article
Andreas Langer, Thomas Zink, De Rham-Witt cohomology and displays. Doc. Math. 12 (2007), pp. 147–191DOI 10.4171/DM/222