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Some consequences of the Riemann hypothesis for varieties over finite fields

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Abstract

We deduce from Deligne's form of the Riemann hypothesis and the hard Lefschetz theoremin l-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. Deligne, P.:Lectures at the International Geometry Colloquium. July 4–11, 1973 Cambridge,England

  2. Berthelot, P.: Le théorème de Lefschetz ≪Faible≫ en Cohomologie Cristalline. To appear

  3. Kleiman, S.: Algebraic Cycles and the Weil Conjectures, in Dix Exposés sur la Cohomologie des Schemas, pp. 359–386. Amsterdam: North-Holland 1969

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08540, Princeton, N.J., USA

    Nicholas M. Katz

  2. Department of Mathematics, MIT, Cambridge, Mass., USA

    William Messing

Authors
  1. Nicholas M. Katz
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  2. William Messing
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Katz, N.M., Messing, W. Some consequences of the Riemann hypothesis for varieties over finite fields. Invent Math 23, 73–77 (1974). https://doi.org/10.1007/BF01405203

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  • DOI: https://doi.org/10.1007/BF01405203

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