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Title: On the Injectivity of the Homomorphisms from the Automorphism Groups of Fields to the Outer Automorphism Groups of the Absolute Galois Groups
Authors: HOSHI, Yuichiro
Keywords: 11R32
absolute Galois group
outer automorphism group
Kummer theory
Artin-Schreier theory
Issue Date: Jul-2022
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Start page: 1
End page: 11
Thesis number: RIMS-1962
Abstract: In the present paper, we discuss the injectivity of the natural homomorphism from the automorphism group of a given field to the outer automorphism group of the associated absolute Galois group. We prove that this natural homomorphism is injective in the case where, for instance, the given field may be embedded into the field of fractions of some Noetherian local domain of mixed characteristic.
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