CONTENTS
Chapter 16. Ramification Theory
§16.1. Inertia groups
§16.2. Ramification groups
Chapter 17. The Fundamental Equality
§17.1. The fundamental inequality
§17.2. Ostrowski's theorem
§17.3. Defectless fields
§17.4. Extensions of discrete valuations
Chapter 18. Hensel's Lemma
§18.1. The main variants
§18.2. nth powers
§18.3. Example: complete valued fields
§18.4. Example: power series fields
§18.5. The Krasner-Ostrowski lemma
Chapter 19. Real Closures
§19.1. Extensions of orderings
§19.2. Relative real closures
§19.3. Sturm's theorem
§19.4. Uniqueness of real closures
Chapter 20. Coarsening in Algebraic Extensions
§20.1. Extensions of localities
§20.2. Coarsening and Galois groups
§20.3. Local closedness and quotients
§20.4. Ramification pairings under coarsening
Chapter 21. Intersections of Decomposition Groups
§21.1. The case of independent valuations
§21.2. The case of incomparable valuations
§21.3. Transition properties for Henselity
Chapter 22. Sections
§22.1. Complements of inertia groups
§22.2. Complements of ramification groups
141
141
143
151
151
153
157
158
161
161
164
166
168
170
175
175
177
181
184
187
187
189
190
191
193
193
194
195
199
199
203
Part IV. if-Rings
Chapter 23. /^-Structures
§23.1. Basic notions
§23.2. Constructions of /^-structures
§23.3. Rigidity
§23.4. Demuskin /^-structures
Chapter 24. Milnor if-Rings of Fields
§24.1. Definition and basic properties
§24.2. Comparison theorems
§24.3. Connections with Galois cohomology
209
209
210
213
214
217
217
219
221
Chapter 25. Milnor if-Rings and Orderings 225
Previous Page Next Page