  We prove a functional equation for two projective systems of finite abelian
$p$-groups, $\{\fa_n\}$ and $\{\fb_n\}$, endowed with an action of $\ZZ_p^d$
such that $\fa_n$ can be identified with the Pontryagin dual of $\fb_n$ for all
$n$.
  Let $K$ be a global field. Let $L$ be a $\ZZ_p^d$-extension of $K$ ($d\geq
1$), unramified outside a finite set of places. Let $A$ be an abelian variety
over $K$. We prove an algebraic functional equation for the Pontryagin dual of
the Selmer group of $A$.
