Correspondence theorems for infinite Hopf–Galois extensions

  • Hoan-Phung Bui

    Université Libre de Bruxelles (ULB), Belgium
  • Joost Vercruysse

    Université Libre de Bruxelles (ULB), Belgium
  • Gabor Wiese

    Université du Luxembourg, Esch-sur-Alzette, Luxembourg
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Abstract

This paper extends Hopf–Galois theory to infinite field extensions and provides a natural definition of subextensions. For separable (possibly infinite) Hopf–Galois extensions, it provides a Galois correspondence. This correspondence also is a refinement of what was known in the case of finite separable Hopf–Galois extensions.

Cite this article

Hoan-Phung Bui, Joost Vercruysse, Gabor Wiese, Correspondence theorems for infinite Hopf–Galois extensions. Doc. Math. (2025), published online first

DOI 10.4171/DM/993