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 SpK. We show that there exists a finite separable field extension K' of K, a rigid-analytic space X' K' over SpK' having a strictly semi-stable formal model over the ring of integers of K', and an étale, surjective morphism f : X' K' →X K of rigid-analytic spaces over SpK. This is different from the alteration result of A.J. de Jong [dJ] who does not obtain that f is étale. To achieve this property we have to work locally on X K , i.e. our f is not proper and hence not an alteration.
KeywordsSingular Point Irreducible Component Singular Locus Closed Immersion Smooth Locus
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