Characteristic ideals and Selmer groups

Let A be an abelian variety defined over a global field F of positive characteristic p   and let F/FF/F be a ZpN-extension, unramified outside a finite set of places of F. Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the p-primary Selmer group of A  . To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Zpd-extension Fd/FFd/F and for any Zpd−1-extension contained in FdFd, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Zp[[Gal(F/F)]]Zp[[Gal(F/F)]] in the case A is a constant abelian variety.