MATH-643 / 2 credits

Teacher: Michel Philippe

Language: English

Remark: Spring semester


Only this year


In this course we will describe in numerous examples how methods from l-adic cohomology as developed by Grothendieck, Deligne and Katz can interact with methods from analytic number theory (prime numbers, modular forms etc...).



Analytic Number Theory, Algebraic Geometry, Etale Cohomology.

Learning Prerequisites

Required courses

Basic Number Theory (algebraic and analytic), Algebraic Geometry

Recommended courses

Modular forms

Learning Outcomes

By the end of the course, the student must be able to:

  • Recognize the basic properties of trace functions and how to use these in unconventional settings (outside algebraic geometry)



N. Katz books at PUP (notably "Gauss Sums Kloosterman Sums and Monodromy"); Arizona Winter School "Lectures on Applied l-adic Cohomology"

Ressources en bibliothèque


In the programs

  • Exam form: Oral (session free)
  • Subject examined: Applied l-adic cohomology
  • Lecture: 28 Hour(s)

Reference week