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Let $K$, $L$ be finite extensions of the $p$-adic numbers. Suppose $\chi:G_K\rightarrow L^{\times}$ is crystalline. It is my understanding that if either $K$ or $L=\mathbb{Q}_p$, then $\chi$ must be a ...

Let $K$ be a number field and $A/K$ an abelian variety over it. Can it be that $K(A[n])$ does not contain a primitive $n$-th rooth of unity? If the answer is yes is it always possible to ...

I already created this post on Math Stack Exchange but I was not so sure if this question fits better here. If it is not, I want to apologize in advance and feel free to delete my post. I want to ...