# Tagged Questions

Questions relating to the representations of the absolute Galois group $\mathrm{Gal}(\overline K/K)$ of a number field or of a local field.

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### Tate curve and action of inertia group

I read the answers to this question Clarifying a comment of Serre. However I miss a passage of the second answer and since I can't comment there I have should post a new question. I don't understand ...
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### Galois Representation with $D_{10}$ image

I want to construct an explicit elliptic curve $E$ over a number field $K$ such that $Gal(K(E[l])/K) \cong D_{10}$ where $D_{10}$ is the dihedral group of order 10 and $l$ is a prime number. ...
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### What is : $\ \mathrm{Gal} ( \overline{ \mathbb{Q} } / \mathbb{Q} )$?

In a book, I find the following thing : The natural homomorphism $\mathrm{Gal} ( \overline{\mathbb{Q}} / \mathbb{Q}) \to \displaystyle \lim_ {\longleftarrow n} \mathrm{Gal} (K_n / \mathbb{Q})$ is ...
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### Importance of continuity of Galois representations

So for a one dimensional Galois representation $\rho: G_{\Bbb Q} \to \mathbb C^{\times}$, I know that it must factor through the abelianization of $G_{\Bbb Q}$, which by the Kronecker-Weber theorem is ...
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### Elements of order 2 in the absolute Galois group

So I remember reading once that the only element of $G=Gal(\overline{\Bbb Q} / \Bbb Q)$ that we understand is complex conjugation. Suppose we fix an embedding of $\overline{\Bbb Q}$ into $\Bbb C$. ...
### Identifying the residue field of $\overline{\mathbb{Q}}_p$ with $\overline{\mathbb{F}}_p$
Could anyone epxlain to me how to identify the residue field of $\overline{\mathbb{Q}}_p$ with $\overline{\mathbb{F}}_p$ ? I am basically trying to go from a $p$-adic galois representation of \$G_\...