p-adic numbers and the local-global principle

par Corentin Lambert

lundi 9 févr. 2026, 16:30 → 17:30 Europe/Paris

S435 (UMPA)

The local-global principe (also known as Hasse principle) stipulates that the study of the completions of a number field sould give result about the initial field.For the rational numbers, the usual completion is the field of real number, but the other completions are exactly the p-adic numbers for p a prime number. The aim of this presentation is to introduce you to the world of p-adic numbers and illustrate the Hasse principle with the Hasse-Minkowski theorem.