Year: 2026
Type: preprint
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 $f \colon Y \to X$ that is curve tame over a base $S$, we construct a compactification $\bar{f} \colon \overline{Y} \to \overline{X}$ over $S$ that is numerically tame.
Source: arXiv (Cornell University)
Authors: Hübner, Katharina, Temkin, Michael
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221122380