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First European Congress of Mathematics pp 491–510Cite as

Evidence for a Cohomological Approach to Analytic Number Theory

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Part of the book series: Progress in Mathematics ((PM,volume 3))

Abstract

The first two sections of this note are an expanded version of the lecture at the Congress. We first explain how a cohomological formalism might look, one that would serve the same purposes for zeta functions of number fields and étale or cristalline cohomology for zeta functions of curves over finite fields. After indicating some consequences of the hypothetical formalism that can actually be proved, we explain how very naturally the Riemann hypotheses would ensue. These matters are also discussed in [De2] but in the much more general framework of motives. We thought that it might be useful to make the simple basic ideas available to non experts for motives as well.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Westf. Wilhelms-Universität, Einsteinstr 62, D-48149, Münster, Germany

    Christopher Deninger

Authors
  1. Christopher Deninger
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Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques Fondamentales, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Anthony Joseph  & Rudolf Rentschler  & 

  2. The Weizmann Institute of Science, 76100, Rehovot, Israel

    Anthony Joseph

  3. Mathématiques Bâtiment 425, Université de Paris-Sud, 91405, Orsay Cedex, France

    Fulbert Mignot

  4. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex, France

    François Murat

  5. Laboratoire de Statistique Médicale, Université Paris V, 45, rue des Saints Pères, 75270, Paris Cedex, France

    Bernard Prum

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© 1994 Birkhäuser Verlag

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Deninger, C. (1994). Evidence for a Cohomological Approach to Analytic Number Theory. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics . Progress in Mathematics, vol 3. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9110-3_16

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  • DOI: https://doi.org/10.1007/978-3-0348-9110-3_16

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9911-6

  • Online ISBN: 978-3-0348-9110-3

  • eBook Packages: Springer Book Archive

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