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
3 - The Weil conjectures
Published online by Cambridge University Press: 28 April 2020
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
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!).
- Type
- Chapter
- Information
- Zeta and L-Functions of Varieties and Motives , pp. 44 - 72Publisher: Cambridge University PressPrint publication year: 2020