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The Galois Group Of The Maximal 2-Extension Of A Field, Wenfeng Gao

Digitized Theses

This work is on the structure of the Galois groups of the maximal 2-extensions of a field. This work is closely related to many famous open questions (Galois representations, the elementary conjecture, Fermat prime numbers, the level and u-invariant of a field, etc.).;Let F be a field of characteristic not 2 and {dollar}F\sb{lcub}q{rcub}{dollar} the maximal 2-extension of F. Let {dollar}G\sb{lcub}q{rcub}{dollar} be the Galois group of {dollar}F\sb{lcub}q{rcub}/F.{dollar} This work deals with the connections among the Galois theory of F, the structure of {dollar}G\sb{lcub}q{rcub}{dollar} and the mod 2 Galois cohomology of {dollar}G\sb{lcub}q{rcub}.{dollar};One of the most famous questions about Galois cohomology theory and …