Washington had proven in 1978 that for $q$ a prime ($q \neq p$), if $q^{e_n}$ exactly divides the class number of $\mathbb{Q}_n$, ie the $n$-th layer in the cyclotomic $\mathbb{Z}_p$ extension, then $e_n$ is bounded independent of $n$. Are there analogous (partial) results for (dual of) Selmer groups?
$\begingroup$
$\endgroup$
1
-
1$\begingroup$ I am only aware of the work of Jack Lamplugh. He has an article entitled "An analogue of the Washington-Sinnott theorem for elliptic curves with complex multiplication I." From the list of articles on mathscinet pointing at the one by Washington, I would guess that this is all there is. $\endgroup$– Chris WuthrichCommented Sep 10, 2018 at 8:49
Add a comment
|