All Questions
Tagged with rigid-analytic-geometry sheaf-theory
7 questions
18
votes
1
answer
1k
views
Why do rigid spaces have "not enough points"?
In Brian Conrad's notes
here for the 2007 Arizona winter school, bottom of p18, he says that there is an affinoid rigid-analytic space and a sheaf of abelian groups on it equipped with a non-zero ...
- 585
9
votes
1
answer
370
views
G-topological spaces and locales
Consider the following generalization of topological spaces:
Definition: Let $X$ be a set. A G-topology on $X$ is given by certain distinguished subsets $U \subset X$, called admissible open subsets, ...
user513306
8
votes
1
answer
459
views
why don't (can't?) we sheafify the structure presheaf of an adic space
In the definition of an adic space, usually there is a presheaf defined by first saying what it is on a particular basis of the topology of the underlying space, the so called rational subsets. One ...
- 359
5
votes
1
answer
333
views
Topology of ring of global sections of finite union of affinoid opens in a rigid analytic space
Let $X$ be a rigid analytic space over a non-Archimedean field $k$. If $U_1,\ldots,U_n\subseteq X$ are affinoid opens, then it's usually not clear whether or not the admissible open $U=U_1\cup\cdots\...
- 3,380
2
votes
0
answers
122
views
Norm of sections on $T$-invariant subspace of a homogenous space over $\mathbb{Q}_p$
Let $K=\mathbb{Q}_p$ and $G$ a split reductive group over $K$ with split maximal torus $T$. Furthermore, $X$ is a smooth projective variety over $K$ with a free $G$-action. Let $U \subset X$ be a $T$-...
- 473
2
votes
1
answer
247
views
Quasi-coherent sheaves on affinoid space
From Conrad's notes on rigid geometry:
More specifically, Gabber has given an example of a sheaf of modules $F$ on the closed unit disk $B^1$ such that $F$ is locally a direct limit of coherent ...
user138661
1
vote
0
answers
137
views
The stack $\operatorname{GL}_2/B$
Let $F$ be the functor from the category of affinoid Tate algebras over $\mathbb{Q}_p$ to the category $\mathrm{Sets}$, which maps an affinoid $\operatorname{Spm} R$ to the set of orbits $\...
- 2,907