Correspondence theorems for infinite Hopf–Galois extensions
Hoan-Phung Bui
Université Libre de Bruxelles (ULB), BelgiumJoost Vercruysse
Université Libre de Bruxelles (ULB), BelgiumGabor Wiese
Université du Luxembourg, Esch-sur-Alzette, Luxembourg

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