Topics in arithmetic geometry
MATH-494 / 5 crédits
Enseignant:
Langue: Anglais
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
Dans les plans d'études
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Topics in arithmetic geometry
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Topics in arithmetic geometry
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Semestre: Printemps
- Forme de l'examen: Oral (session d'été)
- Matière examinée: Topics in arithmetic geometry
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
Semaine de référence
| Lu | Ma | Me | Je | Ve | |
| 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:
Cours
Exercice, TP
Projet, autre