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Aug 19, 2022 at 5:28 vote accept Desunkid
Aug 18, 2022 at 15:49 comment added SashaP @Desunkid That last statement is a part of the explanation of how to construct examples when the sequence is not right exact, and I took $L$ to be a particular finite extension in the 3rd to last paragraph. I think that $A(L)\otimes \mathbb{Z}_p$ is not finitely generated for every $L$ not finite over $\mathbb{Q}_p$.
Aug 18, 2022 at 13:37 comment added Desunkid Thanks for your answer. In the last statement $\mathrm{rk}(A(L)\otimes\bZ_p)=\dim A\cdot [L:\mathbb{Q}_p]$, how about $L$ is infinite extension of $\mathbb{Q}_p$?
Aug 18, 2022 at 12:59 history answered SashaP CC BY-SA 4.0