On quasi-purity of the branch locus
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 → X...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2020
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| In: |
Manuscripta mathematica
Year: 2018, Volume: 161, Issue: 3, Pages: 325-331 |
| ISSN: | 1432-1785 |
| DOI: | 10.1007/s00229-018-1096-y |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s00229-018-1096-y
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| Author Notes: | Alexander Schmidt |
| Summary: | 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 → 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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| Item Description: | Published online: 6 December 2018 Gesehen am 06.03.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1432-1785 |
| DOI: | 10.1007/s00229-018-1096-y |