Kummer-faithfulness for function fields

Publication date: 8 March 2023

Abstract: We investigate a function field analogue of the notion of Kummer-faithful fields. We introduce a notion of Drinfeld-Kummer-faithful (DKF) fields using Drinfeld modules. A sufficient condition for a Galois extension of a function field to be DKF is provided in terms of ramification theory. Some examples of DKF fields are also given. The construction of these examples emulates Ozeki and Taguchi's examples of highly Kummer-faithful fields.

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Ramification and extension theory (11S15) Field arithmetic (12E30)

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