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Rigid Analytic Flatificators
Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f : Y → X be a map of K-affinoid varieties. We prove that for each point x ∈ X, either f is flat at x, or there exists, at least locally around x, a maximal locally closed analytic subvariety Z ⊂ X containing x, such that the base change f−1(Z)→ Z is flat at x, and, moreover, g−1(Z) has again this property ...
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The idea is simple: we want to develop a theory of analytic manifolds and spaces over fields equipped with an arbitrary complete valuation. Of course, it is a standard fact that such a field must be either R, C, or a field with a nonarchimedean valuation, so what we really mean is that we want to develop a theory of nonarchimedean analytic spaces. Doing this näıvely (i.e., defining manifolds in...
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ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2019
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748019000501