Questions tagged [p-adic-hodge-theory]
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218 questions
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classifying reducible 2-dimensional mod-p Galois representations
I want to classify reducible $2$-dimensional mod-$p$ Galois representations of a field $E$ of characteristic $p > 0$ (i.e. representations $G_E = \mathrm{Gal}(E^{sep}/E) \to GL_n(\mathbf{F}_p)$)
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$(\varphi, \Gamma)$-modules, geometric interpretation $D_{diff}$
Could anyone explain to me the first paragraph of page 29 (IV.4.1) of this course of L. Berger:
http://perso.ens-lyon.fr/laurent.berger/articles/article05.pdf
Specifically, I would like to ...
- 11
5
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1
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Reference for $p$-adic Hodge theory with coefficients
Let $K$ be a $p$-adic field and $L$ be a finite or infinite extension (maybe algebraic ?) of $\mathbb{Q}_p$.
Is there a reference for $p$-Hodge theory for representations $\rho : Gal_K \rightarrow ...
- 6,924
7
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1
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showing that abelian varieties are de Rham *without* showing that they are crystalline
If $X$ is a smooth projective variety over a $p$-adic field $K$, then Faltings' Theorem says that the etale cohomology of $X_{\overline{K}}$ is crystalline.
There have been various steps towards this ...
- 11
5
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1
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632
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Psi operator on Phi-Gamma modules
This is a question about the base-rings appearing in the the theory of $(\varphi, \Gamma)$-modules in $p$-adic Hodge theory.
Let $p$ be prime, $n \ge 1$, and let
$$ \mathbf{A}_{\mathbf{Q}_p}^{\dagger,...
- 6,924
13
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1
answer
3k
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p-adic Hodge theory for varieties defined over \C _p ?
I have a question on p-adic Hodge theory:
When e.g. $X$ is a smooth proper scheme over a finite extension $K$ of $\mathbf{Q}_{p}$ then e.g. one variant of $p$-adic Hodge theory says that there is a ...
- 5,504
6
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0
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590
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Semistable minimal model of a $K3$-surface and the special fibre
Suppose that $K$ is a $p$-adic field, that is a field of characteristic $0$ whose ring of integers is a complete discrete valuation ring $\mathcal O_K$ and with residue field $k$ (algebraic closed) of ...
7
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0
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570
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Which de Rham representations are trianguline?
Let $K/\mathbf{Q}_p$ be a finite extension, and let $V$ be an $n$-dimensional $\overline{\mathbf{Q}_p}$-vector space with a continuous action of $G_K$. Suppose $V$ is de Rham, so potentially ...
- 13.1k
1
vote
0
answers
610
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lefschetz hyperplane theorem in positive characteristic
The proof of the Lefschetz Hyperplane theorem over $\mathbb{C}$ is well-known, and relies on Hodge theory in an important way. Does there exist an analogue of this theorem in positive characteristic, ...
- 3,779
15
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1
answer
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What is the classification of characters in $p$-adic Hodge theory?
Let $K$ be a $p$-adic field and $\chi : Gal_K \rightarrow \mathbb{Q}_p^\times$ be a character. I know that $\chi$ is Hodge-Tate of weight $0$ iff $\chi(I_K)$ is finite (by Sen's theory), and that it ...
- 6,924
11
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0
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807
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Torelli-like theorem for K3 surfaces on terms of its étale cohomology
Is there a proof of a Torelli-like Theorem for a K3-surface over any field (non complex) in terms of its etale or crystalline cohomology?
For example: If $K\ne \mathbb{C} $ and $X\rightarrow \...
7
votes
0
answers
491
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"Nontrivial" singular points on the eigencurve?
Let $\mathscr{C}$ be the Coleman-Mazur-Buzzard eigencurve of some fixed tame level $N$. Are there any known examples of a singular point $x\in \mathscr{C}$ which lies in a unique irreducible ...
- 13.1k
2
votes
1
answer
466
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Minimal semistable model for K3-surfaces.
I wonder if a semistalbe K3 surface over a $p$-adic field has a minimal semistable model. I guess yes but I do not find any reference.
Also, if we have a semistable K3 surface with a log structure, ...
- 656
3
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0
answers
204
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Hodge filtration over $\mathbb Z_p$
Let $p$ be a prime number.
Let $X\to\operatorname{Spec}\mathbb Z_p$ be smooth and proper. Is it true that
the map $H^i(X,\Omega^{\bullet\geq j}_{X/\mathbb Z_p})\to H^i(X,\Omega^\bullet_{X/\mathbb Z_p})...
- 2,842
8
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0
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315
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simple proof of relation between H^1 crystalline and Dieudonne module?
Hi,
Let $k$ be a perfect field of characteristic $p > 0$. Let $A/k$ be an abelian variety. Then the first crystalline cohomology group of $A$ with respect to $W(k)$ (= Witt vectors) is canonically ...
- 2,842
1
vote
1
answer
459
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Submodule of a Kisin module
By M. Kisin, let $k$ be an algebraically closed field of characteristic $p$, and $K$ be a totally ramified extension of $B(k)$, the fraction field of the Witt vector ring $W(k)$, the category of ...
- 1,091
0
votes
0
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391
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the definition of pro-infinitesimal thickenings
Let $R$ be a ring and $A$ and $R$-algebra. A pro-infinitesimal thickening of $R$ is a pair $(D, \theta)$ such that $\theta: D \rightarrow R$ is surjective and $D$ is separated and complete for the $I:=...
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11
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1
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648
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Are D_dR and D_st "potentially comparable"?
Suppose we have a de Rham Galois representation $G_K\rightarrow GL(V)$ for some $p$-adic field $K$ and some finite dimensional vector space $V$ over $\mathbf{Q}_p$. Then it is a theorem that there is ...
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