Alexander Schmidt: On quasi-purity of the branch locus

       Author: Alexander Schmidt
       Title:  On quasi-purity of the branch locus
       in: Manuscripta Math. 161 (2020), 325-331

       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 XL of X in L which ramifies in the scheme morphism XL→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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