Seminario Dottorato 2023/24 - Pietro Vanni (13.03.2024)

For each prime p, p-adic numbers form an extension of the rational numbers that, being topologically complete, allows one to use analytic methods in arithmetic. In this talk I will introduce p-adic numbers outlining their basic properties and the role they play in number theory. Then I will give an idea on how one can employ p-adic numbers to study algebraic varieties (i.e. systems of polynomial equations) in characteristic p.