Hartl Semi-stable models for rigid-analytic spaces-猫眼课题宝

刚性解析空间的 Hartl 半稳定模型

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2003

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U. Hartl

Let R be a complete discrete valuation ring with field of fractions K and let XK be a smooth, quasi-compact rigid-analytic space over Sp K . We show that there exists a finite separable field extension K ′ of K , a rigid-analytic space X′ K ′ over Sp K ′ having a strictly semi-stable formal model over the ring of integers of K ′, and an étale, surjective morphism f : X′ K ′ −→ XK of rigid-analytic spaces over Sp K . 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 XK , i.e. our f is not proper and hence not an alteration.