On an elementary Abelian \(p\)-extension of a multidimensional local field
Let \(F\) be an \(n\)-dimensional local field of characteristic 0 with first residue class field of prime characteristic \(p\). The author generalizes Shafarevich's canonical basis for the multiplicative group of one- dimensional local fields to the topological Milnor groups \(K_ m^{top}(F)\). Then he constructs the maximal elementary abelian \(p\)- extension of the field \(\mathbb{Q}_ p\{\{t_ 1\},\ldots,\{t_{n-1}\}\}\) by means of formal Lubin-Tate groups. Finally he generalizes a theorem of Dwork about the Artin symbol to \(n\)-dimensional local fields and applies this generalization to Kummer extensions.
maximal elementary abelian \(p\)-extension
scientific article; zbMATH DE number 10873