It's known that local fields can be defined as a non-discrete, Hausdorff (equivalently non-indiscrete), locally compact, topological field, which is the same as non-trivial (i.e. neither discrete nor indiscrete) locally compact topological field.

In particular, local fields can be defined without mentioning absolute values. For me, absolute values involve the non-natural group $\mathbb{R}$ as the codomain, making those valued fields bounding to $\mathbb{R}$ in some way.

We know global fields can be defined using local fields and absolute valuations. Is it possible to define global fields as certain type of topological fields without mentioning any absolute value?

It's known that local fields can be defined as a non-discrete, Hausdorff (equivalently non-indiscrete), locally compact, topological field, which is the same as non-trivial (i.e. neither discrete nor indiscrete) locally compact topological field.

In particular, local fields can be defined without mentioning absolute values. For me, absolute values involve the non-natural group $\mathbb{R}$ as the codomain, making those valued fields bounding to $\mathbb{R}$ in some way.

We know global fields can be defined using local fields and absolute valuations. Is it possible to define global fields as certain type of topological fields without mentioning any absolute value?

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edit: "without mentioning any absolute value" means that the axiomatic definition of global field doesn't involve absolute values.