Inventiones mathematicae

, Volume 23, Issue 1, pp 73–77 | Cite as

Some consequences of the Riemann hypothesis for varieties over finite fields

  • Nicholas M. Katz
  • William Messing
Article

Abstract

We deduce from Deligne's form of the Riemann hypothesis and the hard Lefschetz theoreminl-adic cohomology the corresponding facts for any “reasonable” cohomology theory, in particular for crystalline cohomology, and give some applications to algebraic cycles.

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References

  1. 1.
    Deligne, P.:Lectures at the International Geometry Colloquium. July 4–11, 1973 Cambridge,EnglandGoogle Scholar
  2. 2.
    Berthelot, P.: Le théorème de Lefschetz ≪Faible≫ en Cohomologie Cristalline. To appearGoogle Scholar
  3. 3.
    Kleiman, S.: Algebraic Cycles and the Weil Conjectures, in Dix Exposés sur la Cohomologie des Schemas, pp. 359–386. Amsterdam: North-Holland 1969Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Nicholas M. Katz
    • 1
  • William Messing
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsMITCambridgeUSA

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