# Questions tagged [rigid-analytic-spaces]

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### Reference request: Integral rigid spaces

Is there a notion of integral rigid spaces which mirrors the theory of integral schemes? For instance, let $B$ be an integral affinoid algebra over a non-Archimedean field $k$. Then are the affinoid ...
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### Rational functions on an affinoid subset of $\mathbb{P}^1$

In Van der Put's Rigid analytic geometry and its applications, he's trying to define holomorphic functions on an affinoid subset of $\mathbb{P}^1/K$ as follows, where $(K, |\cdot|)$ is an ...
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### Smooth affinoid rigid-analytic spaces over $\mathbb C_{p}$

Are there any examples of smooth affinoid rigid-analytic spaces $X$ over $\mathbb C_{p}$, which are not the base-change $X=Y_{\mathbb C_{p}}$ of a smooth rigid-analytic variety $Y$ over a finite ...
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### Strong G-Topology on affinoid varieties

I have a question about the strong G-topology of an affinoid variety. In particular let $X=Sp(A)$ be an affinoid variety and we consider analytic functions $f_1,...,f_m\in A$ on X, having no commom ...
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### When is the zero set of a multivariate $p$-adic power series algebraic?

Let $f = f(z_1, \dots, z_n)$ be a power series in $n$ variables with coefficients in the $p$-adic integers $\mathbb{Z}_p$. Let $g(z_1, \dots, z_n) = f(pz_1, \dots, pz_n)$, so that $g$ converges on all ...
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1 vote
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### Lifting points via étale morphism of adic spaces

This question was suggested to me during the reading of Huber's book about Etale Cohomology of Adic Spaces. I formulate this question here in the context of adic spaces, but I think, since a morphism ...
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### Structure Sheaves of Rigid Analytic Spaces: What is the right Value Category?

Let $K$ be a complete non-archimedean field and let $X$ be an affinoid $K$-space. Then the structure sheaf $\mathcal O_X$ of $X$ is defined first on the "weak Grothendieck topology", ie on affinoid ...
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### What is a ring $R$ s.t. $Spa(\mathbb{Z},\mathbb{Z})=Spec R$

The adic spectrum $Spa(\mathbb{Z},\mathbb{Z})$ looks as follows: First, there is a point for every prime ideal $\mathfrak{p}\subset\mathbb{Z}$, corresponding to the valuation given by the composition ...
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