Fine Selmer groups and ideal class groups

Let K be a number field, let A an abelian variety defined over and $$K_\infty /K$$ uniform p-adic Lie extension. We compare several arithmetic invariants of Iwasawa modules ideal class groups on the one side fine Selmer varieties other side. If $$ contains sufficiently many p-power torsion points A, then we can ranks $$\mu -invariants these algebra. In special cases (e.g. multiple $$\mathbb {Z}_p$$ -extensions), also prove relations between suitably generalised $$\lambda two types modules. literature, different kinds have been introduced for groups. define analogues both concepts resulting invariants. order to obtain some our main results, new asymptotic formulas growth in -extensions.