Abstract

Let R, , . . . . iTC be p-adic closures of a field K. In this paper we investigate the behavior of the ‘field K, = KP’ n n K: n K(c,+ 1, . . . . cr ~,+,?I are automorphisms in the absolute Galois group G(K) of K which are chosen at random and where J?( CT~ + I ) . . . . ge + ,,,) is the fixed field of C e+ 17 ...9 gc+/n in the algebraic closure k of K. More precisely, the compact group G(K)‘+,’ is equipped with a unique normalized Haar measure (with respect to the Krull topology on G(K)). We prove :

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