Some consequences of the Riemann hypothesis for varieties over finite fields

Nicholas M. Katz; William Messing

doi:10.1007/BF01405203

Some consequences of the Riemann hypothesis for varieties over finite fields

Nicholas M. Katz, William Messing

Mathematics

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187 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	73-77
Number of pages	5
Journal	Inventiones Mathematicae
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/BF01405203
State	Published - Mar 1 1974

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Some consequences of the Riemann hypothesis for varieties over finite fields

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