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Results tagged with rigid-analytic-geometry
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user 345
rigid analytic varieties, affinoid varieties, strictly convergent power series over non-archimedean fields
7
votes
1
answer
493
views
Are admissible open subsets of an affinoid space of countable type?
A rigid analytic space $Y$ over a complete non-archimedean valued field $k$ is said to be of countable type if it has a countable (possibly finite) admissible covering by affinoids over $k$.
Suppos …
- 3,545
16
votes
D-modules on rigid analytic spaces
Yes. Although it is only beginning to be developed.
You probably want to start with Berthelot: D-modules arithmétiques I : Opérateurs différentiels de niveau fini and Introduction à la théorie arithm …
- 3,545
1
vote
1
answer
755
views
What are in units of an affinoid algebra?
Suppose that $K$ is a complete local field and $A$ is an affinoid $K$-algebra. Is there a known way to produce an explicit description of the units of $A$?
Here is what I already know: write $A^\circ …
- 3,545
9
votes
1
answer
1k
views
Reference Request: Vector bundles in rigid analytic geometry
In algebraic geometry it is well-known (see Hartshorne Exercise II.5.16 for example) that there is a 1-1 correspondence between rank $n$ (geometric) vector bundles $\pi\colon Y\to X$ on a scheme $X$ a …
- 3,545
4
votes
Accepted
What's the relation between pseudo-compact and admissible rings?
Neither of these properties implies the other:
There is an admissible algebra that is not pseudo-compact
If $A$ is a ring with the discrete topology that is not artinian then it is admissible but not …
- 3,545