Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 9
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Borger, James and Grinberg, Darij 2016. Boolean Witt vectors and an integral Edrei–Thoma theorem. Selecta Mathematica, Vol. 22, Issue. 2, p. 595.

    Tikaradze, Akaki 2016. Hochschild Cohomology of Deformation Quantizations over ℤ/p n ℤ. Algebras and Representation Theory, Vol. 19, Issue. 1, p. 209.

    Cuntz, Joachim and Deninger, Christopher 2015. Witt vector rings and the relative de Rham Witt complex. Journal of Algebra, Vol. 440, p. 545.

    Hesselholt, Lars 2015. The big de Rham–Witt complex. Acta Mathematica, Vol. 214, Issue. 1, p. 135.

    Langer, Andreas and Zink, Thomas 2015. Comparison between overconvergent de Rham-Witt and crystalline cohomology for projective and smooth varieties. Mathematische Nachrichten, Vol. 288, Issue. 11-12, p. 1388.

    Berthelot, Pierre Esnault, Hélène and Rülling, Kay 2012. Rational points over finite fields for regular models of algebraic varieties of Hodge type ࣙ1. Annals of Mathematics, Vol. 176, Issue. 1, p. 413.

    Davis, Christopher Langer, Andreas and Zink, Thomas 2012. Overconvergent Witt vectors. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2012, Issue. 668, p. 1.

    Borger, James 2011. The basic geometry of Witt vectors. II: Spaces. Mathematische Annalen, Vol. 351, Issue. 4, p. 877.

    Rognes, John 2009. New topological contexts for Galois theory and algebraic geometry (BIRS 2008). p. 401.

  • Journal of the Institute of Mathematics of Jussieu, Volume 3, Issue 2
  • April 2004, pp. 231-314


  • Andreas Langer (a1) and Thomas Zink (a1)
  • DOI:
  • Published online: 01 April 2004

We construct a relative de Rham–Witt complex $W\varOmega^{\cdot}_{X/S}$ for a scheme $X$ over a base scheme $S$. It coincides with the complex defined by Illusie (Annls Sci. Ec. Norm. Super.12 (1979), 501–661) if $S$ is a perfect scheme of characteristic $p>0$. The hypercohomology of $W\varOmega^{\cdot}_{X/S}$ is compared to the crystalline cohomology if $X$ is smooth over $S$ and $p$ is nilpotent on $S$. We obtain the structure of a $3n$-display on the first crystalline cohomology group if $X$ is proper and smooth over $S$.

AMS 2000 Mathematics subject classification: Primary 14F30; 14F40

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
Please enter your name
Please enter a valid email address
Who would you like to send this to? *