an:01945281
Zbl 1099.14010
Hartl, Urs T.
Semi-stable models for rigid-analytic spaces
EN
Manuscr. Math. 110, No. 3, 365-380 (2003).
00093146
2003
j
14G22
Summary: Let \(R\) be a complete discrete valuation ring with field of fractions \(K\) and let \(X_K\) be a smooth, quasi-compact rigid-analytic space over \(\text{Sp}\,K\).
We show that there exists a finite separable field extension \(K'\) of \(K\), a rigid-analytic space \(X_{K'}'\), over \(\text{Sp} \,K'\) having a strictly semi-stable formal model over the ring of integers of \(K'\), and an ??tale, surjective morphism \(f:X_{K'}'\to X_K\) of rigid-analytic spaces over \(\text{Sp}\,K\). This is different from the alteration result of \textit{A. J. de Jong} [Publ. Math., Inst. Hautes ??tud. Sci. 83, 51--93 (1996; Zbl 0916.14005)] who does not obtain that \(f\) is ??tale. To achieve this property we have to work locally on \(X_K\), i.e. our \(f\) is not proper and hence not an alteration.
Zbl 0916.14005