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<p>Extensions of higher local fields determined by certain matrix equations introduced by E. Inaba are studied. It is proved that any extension decomposable into a tower of Artin–Schreier extensions can be embedded into an Inaba extension that is a composite of the given extension and another Inaba extension. Furthermore, any p-extension with elementary Abelian Galois group can be embedded into an extension with the Galois group isomorphic to a group of unipotent matrices over a field with p elements.</p>

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On the Inaba Extensions of Two-Dimensional Local Fields of Mixed Characteristic

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • I. B. Zhukov,
  • O. Yu. Ivanova

摘要

Extensions of higher local fields determined by certain matrix equations introduced by E. Inaba are studied. It is proved that any extension decomposable into a tower of Artin–Schreier extensions can be embedded into an Inaba extension that is a composite of the given extension and another Inaba extension. Furthermore, any p-extension with elementary Abelian Galois group can be embedded into an extension with the Galois group isomorphic to a group of unipotent matrices over a field with p elements.