Abstract
Let k be a field, K/k finitely generated and L/K a finite, separable extension. We show that the existence of a k-valuation on L which ramifies in L/K implies the existence of a normal model X of K and a prime divisor D on the normalization \(X\_L\) of X in L which ramifies in the scheme morphism \(X\_L\rightarrow X\). Assuming the existence of a regular, proper model X of K, this is a straight-forward consequence of the Zariski–Nagata theorem on the purity of the branch locus. We avoid assumptions on resolution of singularities by using M. Temkin’s inseparable local uniformization theorem.
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Acknowledgements
The author thanks A. Holschbach for helpful discussions and for providing Example 2.2. Moreover, we thank K. Hübner for her comments on a preliminary version of this article.
