Topics in arithmetic geometry
MATH-494 / 5 credits
Teacher:
Language: English
Remark: pas donné en 2023-24
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:
- Demonstrate an understanding of 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
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Topics in arithmetic geometry
- 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: Topics in arithmetic geometry
- 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: Topics in arithmetic geometry
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
Reference week
| Mo | Tu | We | Th | Fr | |
| 8-9 | |||||
| 9-10 | |||||
| 10-11 | |||||
| 11-12 | |||||
| 12-13 | |||||
| 13-14 | |||||
| 14-15 | |||||
| 15-16 | |||||
| 16-17 | |||||
| 17-18 | |||||
| 18-19 | |||||
| 19-20 | |||||
| 20-21 | |||||
| 21-22 |
Légendes:
Lecture
Exercise, TP
Project, other