P-adic numbers and applications
Summary
P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Zeta function.
Content
- Construction and arithmetics of p-adics
- Galois theory and the p-adic complex numbers
- p-adic analysis
- Zeta functions and rationality
- p-adic manifolds and integration
Learning Prerequisites
Recommended courses
- Rings and modules
- Galois theory
- Introduction to differentiable manifolds
Learning Outcomes
By the end of the course, the student must be able to:
- understand the construction and basic theory of p-adic numbers, as well as being able to do calculations involving them.
Teaching methods
course ex-cathedra and exercises
Assessment methods
oral
Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: P-adic numbers and applications
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: P-adic numbers and applications
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: P-adic numbers and applications
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks