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

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.