Inventiones mathematicae

, Volume 23, Issue 1, pp 73–77

Some consequences of the Riemann hypothesis for varieties over finite fields


  • Nicholas M. Katz
    • Department of MathematicsPrinceton University
  • William Messing
    • Department of MathematicsMIT

DOI: 10.1007/BF01405203

Cite this article as:
Katz, N.M. & Messing, W. Invent Math (1974) 23: 73. doi:10.1007/BF01405203


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.

Copyright information

© Springer-Verlag 1974