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7

A Galois representation $\rho_\ell:\operatorname{Gal}(\bar{\mathbb Q}_{\ell}/\mathbb Q_{\ell})\longrightarrow\operatorname{GL}_2(\mathbb Q_{\ell})$ can be semistable (technically $B_{st}$-admissible in the sense of Fontaine). A Galois representation $\bar{\rho}_\ell:\operatorname{Gal}(\bar{\mathbb Q}_{\ell}/\mathbb Q_{\ell})\longrightarrow\operatorname{GL}_2(...


2

I think the group $(\mathbf{Q}_p/\mathbf{Z}_p)\oplus\mathbf{Z}[\tfrac1p]$ does the job, i.e. $$ \mathrm{Hom}((\mathbf{Q}_p/\mathbf{Z}_p)\oplus\mathbf{Z}[\tfrac1p],A(\bar K))\cong B(A). $$ Indeed, let $A(\bar K)_{\mathrm{tor}}$ be the torsion subgroup of $A(\bar K)$. We have a short exact sequence $$ 0\rightarrow A(\bar K)_{\mathrm{tor}}\rightarrow A(\bar K)\...


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