The Galois Group of a Multidimensional Local Field of Positive Characteristic

On the maximal unramified p-extension of an algebraic number field.

“…This non-abelian theory allows us to obtain a formula for the Iwasawa -invariants of a finite normal p-extension even if this extension is not of CAf-type in eontrast to Kida's formula [9]. For the following see also Smith [16] and especially MeFnikow and Sharomet [14]. The group theoretical part 1.…”

Inertia groups and abelian surfaces

“…Let H denote the absolute Galois group of k((t)), and letˆ denote the character group of the group of all roots of unity in k. Then ∼ = =p Z . By Theorem 1 in Section 2 of [14] (see also [10]), H is a semidirect product of a (normal) subgroup W byˆ , where W contains an infinite set J with the following universal property. If S is a pro-p-group with a continuous homomorphism → Aut(S), then every map J → S that sends all but finitely many elements of J to the identity extends uniquely to a continuous homomorphism W → S that commutes with the actions ofˆ .…”

“…Our proof follows [14]. Let H denote the absolute Galois group of k((t)), and letˆ denote the character group of the group of all roots of unity in k. Then ∼ = =p Z .…”