Let $E$ be an elliptic curve defined over $F$ with CM by $\mathcal{O}_K$ where $K$ is an imaginary quadratic field. We may assume the $F$ contains $K$ and also contains the $p$-division points, where $p$ is a good ordinary prime. When $K$ has class number 1, Schnepps' (and Gillard’s) results tell us that the $\mu$-invariant of the dual Selmer over the division field extension (the split prime) is zero. Is it reasonable to believe that the $\mu$-invariant for the dual Selmer over the cyclotomic extension is zero as well for a CM elliptic curve?
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1$\begingroup$ This question has been addressed by Burungale and Hida for anticyclotomic extensions in "p-rigidity and Iwasawa $\mu$-invariants" I don't think it has been studied for the cyclotomic extension. $\endgroup$– user130124Commented Jun 21, 2019 at 16:32
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$\begingroup$ Just noted this questoin. I think it is a duplicate of mathoverflow.net/questions/59294/… $\endgroup$– Chris WuthrichCommented Nov 16, 2020 at 9:42
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