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Questions tagged [rigid-analytic-spaces]

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(Sanity check) the adic spectrum $\operatorname{Spa}(\mathbb{Z}, \mathbb{Z})$

I am following Scholze's and Weinstein's notes on $p$-adic geometry on http://www.math.uni-bonn.de/people/scholze/Berkeley.pdf, example 2.3.6 (page 18 as of this moment bar any updates). $\...
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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 are Robba rings and why are they important?

If we study $p$-adic Galois representations we come across the so called "Robba rings", defined as the ring of Laurent series which converge in some annulus $\{z| \,\,R<|z|<1\}$ for some ...
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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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From sheaf torsors to geometric bundles on schemes

$\DeclareMathOperator{\Spec}{Spec}$ $\DeclareMathOperator{\Sym}{Sym}$ $\newcommand{\func}{\mathcal{O}}$ $\newcommand{\M}{\mathcal{M}}$ It is well known that the notions of locally free $\func_X$-...
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Local ring of an affinoid K-space $Spec A$ is not $A_m$

Let $X$ be an affinoid K-space. That is $X=Spec A$ where $A$ is a quotient of the Tate algebra. In Bosch 'lectures on Formal and Rigid Geometry' we find the curious statement that the canonical map $...
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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 ...