# Tagged Questions

**2**

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**0**answers

103 views

### Bloch Kato Exponential as formal lie group exponential

Let $K$ be a $p$-adic field and $V$ a $p$-adic representation. In their paper on tamagawa numbers of motives, Bloch and Kato define an exponential map as the connecting homomorphism
$$DR(V) ...

**6**

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**0**answers

125 views

### 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 $G_E = \mathrm{Gal}(E^{sep}/E) \to GL_n(\mathbf{F}_p)$)
$$
...

**1**

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**0**answers

97 views

### $(\varphi, \Gamma)$-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 ...

**5**

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**2**answers

282 views

### 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 ...

**5**

votes

**1**answer

225 views

### 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
$$ ...

**5**

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**0**answers

231 views

### 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 ...

**10**

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**0**answers

389 views

### Why does $H^i(X_{ét},\mathbb{Q}_p)$ have a Hodge-Tate structure?

Let $X$ be a variety over a $p$-adic field $K$.
Is there a simple or intuitive explanation of why the $G_K$ representation $H^i(X_{ét},\mathbb{Q}_p)$ is Hodge-Tate? More precisely, why do the powers ...

**12**

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**1**answer

319 views

### 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 ...

**1**

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**1**answer

318 views

### Hodge-Tate weights of etale cohomology

Let $K/\mathbb Q_p$ be a local field, $X/K$ a proper scheme with semi-stable reduction.
Question: What is the possible range of Hodge-Tate weights of the etale cohomology $H^i(X_{\overline K}, ...