Abstract
We prove in arbitrary characteristic that an immediate valued algebraic function field F of transcendence degree 1 over a tame field K is contained in the henselization of K(x) for a suitably chosen x ∈ F. This eliminates ramification in such valued function fields. We give generalizations of this result, relaxing the assumption on K. Our theorems have important applications to local uniformization and to the model theory of valued fields in positive and mixed characteristic.
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