منابع مشابه
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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We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem [Ber, Theorem 4.5.1], which says there are no nonconstant rigid analytic maps from the affine line to non-singular projective curves of positive genus, ...
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Let p be a prime > 3 and consider the Tate algebra A := Q p z defined to be the Banach algebra of formal power series over Q p that converge on the closed unit disk B[0, 1] ⊆ C p with the supremum norm ||f || := sup z∈B[0,1] |f (z)| for f ∈ A. Equivalently, we have (0.1) A = f (z) = ∞ k=0 a k z k a k ∈ Q p and lim k→∞ a k = 0 and the norm is given by (0.2) ||f || = sup k |a k |, for f = ∞ k=0 a...
متن کاملOverview of Rigid Analytic Geometry
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: The Quarterly Journal of Mathematics
سال: 1999
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qjmath/50.199.321