All Questions
Tagged with reference-request rigid-analytic-geometry
17 questions
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Reference Request: Preservation of étale maps under rigid analytic GAGA
Let $K$ be a finite extension of $\mathbb{Q}_p$. As the title says, I am looking for a reference in which it is shown that given an étale map $f:X\rightarrow Y$ between smooth algebraic $K$-varieties, ...
- 541
2
votes
0
answers
679
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Roadmap for p-adic geometry
I think some questions asked in similar fashion with this one. I am a master student in mathematics. I have knowledge in algebraic geometry(both in Shafarevich's and Vakil's books), algebraic topology ...
- 21
3
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0
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146
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Looking for a source on Conrad-Gabber's results about spreading out of rigid-analytic families
Brian Conrad and Ofer Gabber have some results that were announced 9 years ago here:
https://www.ihes.fr/~abbes/Gabber/OferGabber.pdf
and there's a talk by Gabber about them here:
https://www.youtube....
- 4,164
3
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Wondering if Monsky-Washnitzer ever published a result claimed to be forthcoming in a later paper
At the very end of the paper Formal Cohomology I by Monsky and Washnitzer, they write the following:
"In some sense, the operator $\psi$ applied to a power series gives it "better
growth ...
- 658
4
votes
1
answer
459
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Motivic cohomology of rigid analytic spaces
There is a satisfactory theory of B1-homotopy theory for rigid analytic spaces defined by Ayoub in the style of Voevodsky, and I'm aware of some work about the corresponding theory of motives, e.g. ...
- 2,054
7
votes
1
answer
325
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Indeterminacy locus of meromorphic maps of rigid analytic spaces
Setup. Let $k$ be an algebraically closed field of characteristic zero. Let $X/k$ be a normal variety, and let $Y/k$ be a proper variety. It is well-known that the indeterminacy locus of a rational ...
- 998
5
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Are affinoid algebras over nontrivially valued fields Jacobson?
It is well-known that for any field $k$ with valuation the Tate algebra $k\{T_1,\dots,T_n\}$ is Jacobson (see Bosch-Güntzer-Remmert for nontrivial valuations; for trivial valuations those are just ...
- 28.2k
8
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551
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Foundational Questions on Adic Spaces
There are some foundational questions on adic spaces that I can't find in the literature. It seems that these questions are pretty natural, so I guess that an answer should be known to the experts in ...
- 2,923
5
votes
2
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596
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generic fibre functor for relative rigid spaces
The classical theory of formal models of rigid analytic spaces due to
Raynaud introduces the category of admissible R-formal schemes for $R$ a
discretely valued ring, which includes locally ...
- 4,070
8
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0
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518
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$p$-adic uniformisation of abelian varieties
In the paper $p$-adic L-functions and $p$-adic periods of modular forms of Greenberg and Stevens $\S3$ page $420$ they make the following statement:
Let $A$ over $\mathbf{Q}_p$ be an abelian variety ...
- 121
5
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1
answer
471
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Rigid analytic geometry in characterstic 0 vs positive characteristic
This question is motivated purely by curiosity. In algebraic geometry there is a major distinction between the world of characteristic $0$ and that of characteristic $p > 0$ with different methods, ...
- 912
3
votes
2
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524
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Product of reduced affinoid spaces over a field is reduced (reference request)
Let $K$ be a field of characteristic zero complete with respect to a non-Archimedean absolute value. Suppose that $A$ and $B$ are two affinoid $K$-algebras. I'd like a reference that will answer the ...
- 408
4
votes
1
answer
685
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Paper of Boutot-Carayol in `Courbes modulaires et courbes de Shimura'
I am trying to obtain a copy of the following
J.-F. Boutot and H. Carayol, Uniformisation p-adique des courbes de Shimura: les
théorèmes de Čerednik et de Drinfel'd , Astérisque No. 196-197 (1991)...
- 910
10
votes
1
answer
504
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Picard group of Drinfeld upper half space
Let $K$ be a $p$-adic field and $\Omega^{(n)}_K$ the $n$-dimensional Drinfeld upper half space over $K$ (which is a rigid analytic space over $K$).
Is the Picard group of $\Omega^{(n)}_K$ known? ...
- 10.5k
9
votes
1
answer
1k
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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 $X$ ...
- 3,545
13
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1
answer
2k
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Reference for rigid analytic GAGA
I'm looking for a reference for the following result.
Theorem. Let $K$ be a complete, non-archimedean field, and let $X/K$ be a projective scheme, with analytification $X^\mathrm{an}$. Then the ...
- 1,838
3
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0
answers
484
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Sheaf of power-bounded elements in rigid analytic geometry
Let $k$ be a field with a non-archimedean complete valuation $|\ |$, $X$ a reduced rigid analytic space over $k$. The presheaf $\mathcal{O}^0$ which to an affinoid $U$ of $X$ attaches the ring $\...
- 26.1k