Global Fields of Finite Type
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We now consider as our base fields global fields k of finite type, i.e., finite extensions k/ℚ or k/F q (x). The results of this chapter form the central part of this book. We are going to study the Galois group Gs of the maximal p-extension of k unramified outside some set of primes S of k, and we investigate in particular how to use the theorems on the structure of the Galois group of the maximal p-extension of a local field derived in the last chapter to get results on Gs.
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