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In this article, we study the pseudo-isomorphism class of the dual fineSelmer group $X$ attached to a $p$-adic Galois deformation whose deformationring $\Lambda$ is isomorphic to the ring of formal power series. By using the"Kolyvagin system" arising from a given Euler system $c$, we shall constructideals $C_i(c)$ of $\Lambda$, and prove that the ideals $C_i(c)$ approximatethe higher Fitting ideals of $X$ under suitable hypothesis. In particular, weshall prove that the ideals $C_i(c)$ arising from the Euler system ofBeilinson-Kato elements determine the pseudo-isomorphism classes of the dualfine Selmer groups attached to ordinary and nearly ordinary Hida deformationssatisfying certain conditions.

Euler systems for Galois deformations and the pseudo-isomorphism class of the dual of fine Selmer groups