Questions tagged [p-adic-hodge-theory]
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14 questions
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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 ...
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2
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congruent number problem [closed]
I am studying the congruent number problem
and I heard that there is a paper by Kazuma Morita
which claims to solve this problem from my colleague.
I saw the paper on his homepage but it is very ...
- 115
59
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0
answers
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Grothendieck's Period Conjecture and the missing p-adic Hodge Theories
Singular cohomology and algebraic de Rham cohomology are both functors from the category of smooth projective algebraic varieties over $\mathbb Q$ to $\mathbb Q$-vectors spaces. They come with the ...
- 149k
32
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1
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$p$-adic Hodge Theory for rigid spaces, after P. Scholze
I was going over P. Scholze's paper on $p$-adic Hodge Theory for rigid analytic varieties.
This question is around the "Poincaré Lemma" in the paper.
Throughout, let $X$ be a proper smooth rigid ...
user113453
16
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1
answer
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Applications of $p$-adic Hodge theory
I am trying to learn $p$-adic Hodge theory. I found some materials explaining main theorems (or aspects) of the theory. However, I could not find references which explaining how to use the theory. ...
7
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1
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How large is Dcris of certain twists of modular forms?
I want to determine $\mathrm D_{\mathrm{cris}}$ of certain twists of the Galois representations attached to modular forms. For one particular twist it is not clear to me how $\mathrm D_{\mathrm{cris}}$...
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7
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0
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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 ...
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6
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1
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Integral Tate-Sen theory
Let $K$ be a finite extension of $\mathbb{Q}_p$, and let $C=\widehat{\overline{K}}$ be the completion of the algebraic closure of $K$. Let $\mathscr{O}_C$ be the ring of integers in $C$, and let $G_K$ ...
- 23k
6
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2
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Topology on $p$-adic period rings in an article by Fontaine, part II
This is a follow-up to this question. See that question for background and relevant notation.
In the answer to that question, it is claimed, if I understand the answer correctly, that a basis of ...
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4
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1
answer
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A definition of a (amalgamated) direct sum
I am wondering about a definition of a direct sum in page $31$ of this paper by R. Liu.
I am following the notations in page $31$ of the above paper. Let $V$ be a crystalline irreducible ...
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3
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1
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Calculation of Frobenius on de Rham cohomology of elliptic curves with good reduction
I'm reading "An introduction to the theory of $p$-adic representations" by Laurent Berger. In the page 14 it says:
Suppose $F$ is an unramified finite extension of $\mathbb Q_p$ and $E$ is ...
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3
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3
answers
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Topology on $p$-adic period ring in an article by Fontaine
Fix a $p$-adic field $K$ with perfect residue field $k.$ Let $\mathcal{C}$ be the completion of the algebraic closure of $K,$ and let $$R = \varprojlim \mathcal{C}/p,$$ where the transition maps in ...
3
votes
1
answer
455
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References for the early history of Fontaine's tilting construction
Scholze attributes the tilting construction for perfectoid rings to Fontaine, who calls it "a classical construction in $p$-adic Hodge theory".
Would anyone happen to know an early reference where ...
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2
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1
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Irreducibility of Tate module (as a Galois representation) of elliptic curves with good reduction
This question is following the previous question.
Definitions:
Suppose $F$ is an unramified finite extension of $\mathbb Q_p$ and $E$ is an elliptic curve defined over $F$ with good reduction. Denote ...
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