Book contents
- Frontmatter
- Contents
- Introduction
- 1 The Riemann zeta function
- 2 The zeta function of a Z-scheme of finite type
- 3 The Weil conjectures
- 4 L-functions from number theory
- 5 L-functions from geometry
- 6 Motives
- Appendix A Karoubian and monoidal categories
- Appendix B Triangulated categories, derived categories, and perfect complexes
- Appendix C List of exercises
- Bibliography
- Index
5 - L-functions from geometry
Published online by Cambridge University Press: 28 April 2020
- Frontmatter
- Contents
- Introduction
- 1 The Riemann zeta function
- 2 The zeta function of a Z-scheme of finite type
- 3 The Weil conjectures
- 4 L-functions from number theory
- 5 L-functions from geometry
- 6 Motives
- Appendix A Karoubian and monoidal categories
- Appendix B Triangulated categories, derived categories, and perfect complexes
- Appendix C List of exercises
- Bibliography
- Index
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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- Zeta and L-Functions of Varieties and Motives , pp. 104 - 141Publisher: Cambridge University PressPrint publication year: 2020