Suppose I have a matrix over the $l$-adic integers $\mathbb{Z}_l$ which is diagonalizable over $\mathbb{Q}_l$. How to classify such matrices by similarity over $\mathbb{Z}_l$?
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$\begingroup$ Can you please kindly provide more info on what are $\mathbb Z_l$ and $\mathbb Q_l$? $\endgroup$V. Mikaelian– V. Mikaelian2025-03-08 11:57:02 +00:00Commented Mar 8 at 11:57
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3$\begingroup$ @V.Mikaelian: $\mathbb{Z}_\ell$ is usually either $\mathbb{Z}/\ell \mathbb{Z}$ or the $\ell$-adic integers. But in the former case what would $\mathbb{Q}_\ell$ mean? :-) Isn't it a rather standard notation? I think it's safe to assume the OP is referring to the $\ell$-adic numbers and integers for some prime $\ell \in \mathbb{N}$. $\endgroup$M.G.– M.G.2025-03-08 12:31:14 +00:00Commented Mar 8 at 12:31
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$\begingroup$ Yes, that was was confusing me, as well. $\endgroup$V. Mikaelian– V. Mikaelian2025-03-08 12:57:27 +00:00Commented Mar 8 at 12:57
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3$\begingroup$ This question is related to mathoverflow.net/questions/314976/… $\endgroup$Paul Broussous– Paul Broussous2025-03-11 08:50:22 +00:00Commented Mar 11 at 8:50
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