Selmer groups over $\Z_p^d$-extensions

Abstract

Consider an abelian variety A defined over a global field K and let L/K be a Z d pextension, unramified outside a finite set of places of K, with Gal(L/K) = Γ. Let Λ(Γ) := Zp[[Γ]] 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 e p -extension.