De Rham-Witt cohomology and displays

  • Andreas Langer

    Mathematics Fakultät für Mathematik University of Exeter Universität Bielefeld Exeter, EX4 4QE Postfach 100131 Devon, UK D-33501 Bielefeld
  • Thomas Zink

    Mathematics Fakultät für Mathematik University of Exeter Universität Bielefeld Exeter, EX4 4QE Postfach 100131 Devon, UK D-33501 Bielefeld
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Abstract

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. 147–191

DOI 10.4171/DM/222