Local Fields

Introduction Basic theory Fields Rings Topological rings The p-adic numbers Valued fields Hensel's lemma Extension of norms Newton polygons Discretely valued fields Teichmüller lifts Witt vectors* Some p-adic analysis Ramification theory for local fields Ramification index and inertia degree Unramified extensions Totally ramified extensions Further ramification theory Some filtrations Multiple extensions Local class field theory Infinite Galois theory Unramified extensions and Weil group Main theorems of local class field theory Lubin–Tate theory Motivating example Formal groups Lubin–Tate extensions Index