Local Fields
Daniel Naylor

Contents
I  Basic Theory
1Absolute values
2Valuation Rings
3The p-adic numbers

II  Complete Valued Fields
4Hensel’s Lemma
5Teichmüller lifts
6Extensions of complete valued fields

III  Local Fields
7Local Fields
8Global Fields

IV  Dedekind domains
9Dedekind domains
10Dedekind domains and extensions
10.1Completions
11Decomposition groups

V  Ramification Theory
12Different and discriminant
13Unramified and totally ramified extensions of local fields
13.1Structure of Units
14Higher Ramification Groups

VI  Local Class Field Theory
15Infinite Galois Theory
Index