Abstract
Consider an abelian variety
A
defined over a global field
K
and let
L/K
be a $\Z_p^d$-extension, unramified outside a finite set of places of
K
, with $\Gal(L/K)=\Gamma$. Let $\Lambda(\Gamma):=\Z_p[[\Gamma]]$ denote the Iwasawa algebra. In this paper, we study how the characteristic ideal of the
Λ(Γ)
-module
X
L
, the dual
p
-primary Selmer group, varies when
L/K
is replaced by a intermediate $\Z_p^e$-extension.