# Questions tagged [rigid-analytic-spaces]

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15 questions
1answer
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### Drinfeld upper half plane admissible open

I have a possibly silly question about the Drinfeld upper half plane. It is "well-know" that if $K$ is a complete local field then $\Omega_K = \mathbb{P}^1(\mathbb{C}_k) \backslash \mathbb{P}^1(K)$ ...
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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 ...
0answers
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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 $\func_X$-...
1answer
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### How to determine the minimum number of edges to form a rigid structure in ${\mathbb R}^d$ ($d = 2,3$)?

Let $x_1,\ldots,x_n$ be $n$ points in ${\mathbb R}^d$ ($d = 2,3$). Then, what is the minimum number of edges to form a rigid structure? Thanks!
1answer
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### What is a symplectic form of the rotation group SO(n)

I need to prove that the Hamiltonian system of the rigid body motion  \begin{cases} \dot{R}_t=P_tJ^{-1},\\ \dot{P}_t=2R_t\Lambda,\quad\text{$\Lambda$ is the Lagrange multiplier}\\ R_t^T R_t-I=0, \...
1answer
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### Laurent domains are affinoid domains

Let $\mathcal{A}$ be a $k$-affinoid algebra, as in Berkovich (1990, Chapter 2), and let $X := \mathcal{M}(\mathcal{A})$. In (loc. cit. 2.2.2) it is claimed that if $q > 0$, and $g \in \mathcal{A}$,...
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### Why a finite set is bounded in a topological ring?

I'm almost sure that this question is really idiot and I'm missing something very trivial. In page 36 of Wedhorn's "Adic Spaces" (https://www2.math.uni-paderborn.de/fileadmin/Mathematik/People/wedhorn/...