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3 - The Weil conjectures

Published online by Cambridge University Press:  28 April 2020

Bruno Kahn
Affiliation:
Institut de Mathématiques de Jussieu-Paris Rive Gauche
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Summary

This chapter is dedicated to the Weil conjectures. They are all proven, except the hardest of them: the “Riemann hypothesis”. An overview of Dwork’s p-adic proof of the rationality of zeta functions of varieties over a finite field is given (obtained before the development of Grothendieck’s cohomological methods!).

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Publisher: Cambridge University Press
Print publication year: 2020

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  • The Weil conjectures
  • Bruno Kahn
  • Book: Zeta and L-Functions of Varieties and Motives
  • Online publication: 28 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108691536.004
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  • The Weil conjectures
  • Bruno Kahn
  • Book: Zeta and L-Functions of Varieties and Motives
  • Online publication: 28 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108691536.004
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • The Weil conjectures
  • Bruno Kahn
  • Book: Zeta and L-Functions of Varieties and Motives
  • Online publication: 28 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108691536.004
Available formats
×