Ido Efrat

Valuations, Orderings, and Milnor -Theory

Part I. Abelian Groups: Preliminaries on abelian groups Ordered abelian groups Part II. Valuations and orderings: Valuations Examples of valuations Coarsenings of valuations Orderings The tree of localities Topologies Complete fields Approximation theorems Canonical valuations Valuations of mixed characteristics Part III. Galois Theory: Infinite Galois theory Valuations in field extensions Decomposition groups Ramification theory The fundamental equality Hensels lemma Real closures Coarsening in algebraic extensions Intersections of decompositions groups Sections Part IV.

On the descending central sequence of absolute Galois groups

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A hasse principle for function fields over pac fields

-rings:

Finitely generated pro-p Galois groups of p-Henselian fields

\kappa

Vanishing of Massey Products and Brauer Groups

-structures Milnor

Filtrations of free groups as intersections

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Compatible valuations and generalized milnor K-theory

-rings of fields Milnor

Pro-P galois groups of function fields over local fields

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Lifting of generating subgroups

-rings and orderings

Single-Valued Massey Products

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