Local Fields  Daniel Naylor  Contents  I  Basic Theory  1 Absolute values  2 Valuation Rings  3 The p adic numbers  II  Complete Valued Fields  4 Hensel s Lemma  5 Teichm ller lifts  6 Extensions of complete valued fields  III  Local Fields  7 Local Fields  8 Global Fields  IV  Dedekind domains  9 Dedekind domains  10 Dedekind domains and extensions  10 1 Completions  11 Decomposition groups  V  Ramification Theory  12 Different and discriminant  13 Unramified and totally ramified extensions of local fields  13 1 Structure of Units  14 Higher Ramification Groups  VI  Local Class Field Theory  15 Infinite Galois Theory  Index  Index