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5 - L-functions from geometry

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

Serre. In the mean time the fundamental contributions of Grothendieck and Deligne are explained: rationality and the functional equation for L-functions of l-adic sheaves in characteristic p, with essentially complete proofs; the theory of weights; and some theorems of Deligne on the Riemann hypothesis (the last of Weil’s conjectures), this time without proof. Notably, one will find an exposition of functional equations of the L-functions developed by Grothendieck, and a more precise statement and fairly complete parts of the proof of Grothendieck and Deligne’s theorem on the rationality and the functional equation of Hasse–Weil L-functions in characteristic > 0, confirming a conjecture of Serre in this case.

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Publisher: Cambridge University Press
Print publication year: 2020

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  • L-functions from geometry
  • Bruno Kahn
  • Book: Zeta and L-Functions of Varieties and Motives
  • Online publication: 28 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108691536.006
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  • L-functions from geometry
  • Bruno Kahn
  • Book: Zeta and L-Functions of Varieties and Motives
  • Online publication: 28 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108691536.006
Available formats
×

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.

  • L-functions from geometry
  • Bruno Kahn
  • Book: Zeta and L-Functions of Varieties and Motives
  • Online publication: 28 April 2020
  • Chapter DOI: https://doi.org/10.1017/9781108691536.006
Available formats
×