Open Math Notes

Resources and inspiration for math instruction and learning

Home Submit FAQ Contact My Notes


Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students. These draft works include course notes, textbooks, and research expositions in progress. They have not been published elsewhere, and, as works in progress, are subject to significant revision. Visitors are encouraged to download and use these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto

contact


Notes by Davide Lombardo from a 2019 course by Tamás Szamuely devoted to Deligne's proof of the Riemann Hypothesis for smooth projective varieties over finite fields. Katz's recent proof of the hypersurface case and Esnault's spectacular application of the integrality theorem are also discussed. The course concludes with a brief survey of the main results of 'Weil II'.

Tamás Szamuely
University of Pisa
Davide Lombardo
University of Pisa

Feedback to the author(s)
Open Math Notes authors welcome substantive, useful feedback that helps them develop and improve their notes. Comments submitted through this site may be posted on the Open Math Notes web pages next to the appropriate Note.

If checked, the author will not see your name or email address.
Limit 2000 characters; Plain text only
Optional; Limit 10M
Optional; Limit 10M