Valuations, orderings, and Milnor K-theory / Ido Efrat.

Efrat, Ido, 1963- author.
Providence, Rhode Island : American Mathematical Society, [2006]
Mathematical surveys and monographs ; no. 124.
Mathematical surveys and monographs, 0076-5376 ; volume 124
1 online resource (305 p.)
Valuation theory.
Ordered fields.
Electronic books.
""Contents""; ""Introduction""; ""Conventions""; ""Part I. Abelian Groups""; ""Chapter 1. Preliminaries on Abelian Groups""; ""Â1.1. General facts""; ""Â1.2. Divisible hulls""; ""Â1.3. Rational ranks""; ""Â1.4. Characters""; ""Chapter 2. Ordered Abelian Groups""; ""Â2.1. Basic properties and examples""; ""Â2.2. Ranks""; ""Â2.3. Cores""; ""Â2.4. Cofinality and infinitesimals""; ""Â2.5. Ordered abelian groups of rank 1""; ""Â2.6. Push-downs""; ""Â2.7. Well-ordered sets""; ""Â2.8. Formal power series""; ""Â2.9. Generalized rational functions""; ""Part II. Valuations and Orderings""
""Chapter 3. Valuations""""Â3.1. Valuation rings""; ""Â3.2. Valuations""; ""Â3.3. Places""; ""Â3.4. Discrete valuations""; ""Chapter 4. Examples of Valuations""; ""Â4.1. Valuations from unique factorization domains""; ""Â4.2. Valuations on power series fields""; ""Â4.3. Gauss valuations""; ""Chapter 5. Coarsenings of Valuations""; ""Â5.1. Coarser and finer""; ""Â5.2. Quotients and compositions of valuations""; ""Â5.3. Coarsenings in the mixed characteristic case""; ""Chapter 6. Orderings""; ""Â6.1. Ordered fields""; ""Â6.2. Examples of orderings""; ""Â6.3. Archimedean orderings""
""Chapter 7. The Tree of Localities""""Â7.1. Localities""; ""Â7.2. Localities on residue fields""; ""Â7.3. The tree structure""; ""Chapter 8. Topologies""; ""Â8.1. Basic properties""; ""Â8.2. Continuity of roots""; ""Â8.3. Bounded sets""; ""Chapter 9. Complete Fields""; ""Â9.1. Metrics""; ""Â9.2. Examples""; ""Â9.3. Completions""; ""Chapter 10. Approximation Theorems""; ""Â10.1. Approximation by independent localities""; ""Â10.2. Approximation by incomparable valuations""; ""Â10.3. Consequences""; ""Chapter 11. Canonical Valuations""; ""Â11.1. Compatible localities""
""Â11.2. S-cores""""Â11.3. Explicit constructions""; ""Â11.4. Existence of valuations""; ""Chapter 12. Valuations of Mixed Characteristics""; ""Â12.1. Multiplicative representatives""; ""Â12.2. λ-adic expansions""; ""Â12.3. p-perfect structures""; ""Â12.4. Rings of Witt vectors""; ""Â12.5. Mixed valuations under a finiteness assumption""; ""Part III. Galois Theory""; ""Chapter 13. Infinite Galois Theory""; ""Chapter 14. Valuations in Field Extensions""; ""Â14.1. Chevalley's theorem""; ""Â14.2. Valuations in algebraic extensions""; ""Â14.3. The Galois action""
""Chapter 15. Decomposition Groups""""Â15.1. Definition and basic properties""; ""Â15.2. Immediateness of decomposition fields""; ""Â15.3. Relatively Henselian fields""; ""Chapter 16. Ramification Theory""; ""Â16.1. Inertia groups""; ""Â16.2. Ramification groups""; ""Chapter 17. The Fundamental Equality""; ""Â17.1. The fundamental inequality""; ""Â17.2. Ostrowski's theorem""; ""Â17.3. Defectless fields""; ""Â17.4. Extensions of discrete valuations""; ""Chapter 18. Hensel's Lemma""; ""Â18.1. The main variants""; ""Â18.2. nth powers""; ""Â18.3. Example: complete valued fields""
""Â18.4. Example: power series fields""
Description based upon print version of record.
Includes bibliographical references (pages 269-274) and index.
Description based on print version record.
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