The Fontaine-Mazur cojectures says that if $\chi : \text{Gal}(\overline{\mathbf{Q}}/\mathbf{Q}) \to \mathbf{Q}_p^\times$ is a character which is unramified almost everywhere and de Rham at $p$ then it appears as sub-quotient of the étale cohomology of some algebraic variety over $\mathbf{Q}$.

My question is : **Can I explicitely find a variety $X$ and integer $r$ such that $\chi$ is a subquotient of $H^i_{\text{ét}}(X_{\overline{\mathbf{Q}}},\mathbf{Q}_p(r))$ ?**

From what I understand $X$ will be of dimension $0$ and thus $i=0$ too. I have found these notes of Fargues : https://webusers.imj-prg.fr/~laurent.fargues/Motifs_abeliens.pdf

They are focused on the much more complicated case where $\mathbf{Q}$ is replaced by any number field and I can't seem to extract the answer to my question. In these notes it says that the Hecke character associated to $\chi$ by class field theory will be of the form $\eta*N^k$ where $\eta$ has finite order and $N$ is the norm (this I am fine with) and this implies that $\chi$ is the $p$-adic étale realization of $M(k)$ where $M$ is the simple Artin motive associated to $\eta$. Unfortunately I don't really know what this last part means and I would really like and explicit variety and understand how the $p$-adic étale cohomology gives rise to our original character.