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Largeness of the wild locus

  • Katharina Hübner
  • Michael Temkin
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Abstract

We show that the wild locus of an étale morphism of smooth adic spaces over an affinoid field is either empty or contains a divisorial point. As a consequence, we establish the equivalence of curve tameness and valuation tameness without using resolution of singularities. Moreover, given a finite étale map of regular schemes f : Y → X that is curve tame over a base S, we construct a compactification f̅ : Y̅ → X̅ over S that is numerically tame.

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Cite

BibTeXRIS
BibTeX
@misc{hubner2026largeness,
  title = {{Largeness of the wild locus}},
  author = {Katharina Hübner and Michael Temkin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11864},
  eprint = {2610.11864},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11864},
}
RIS
TY  - UNPB
TI  - Largeness of the wild locus
AU  - Katharina Hübner
AU  - Michael Temkin
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11864
UR  - https://arxiv.org/abs/2610.11864
AB  - We show that the wild locus of an étale morphism of smooth adic spaces over an affinoid field is either empty or contains a divisorial point. As a consequence, we establish the equivalence of curve tameness and valuation tameness without using resolution of singularities. Moreover, given a finite étale map of regular schemes f : Y → X that is curve tame over a base S, we construct a compactification f̅ : Y̅ → X̅ over S that is numerically tame.
ER  -