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In our previous work, by using Kolyvagin derivatives of elliptic units, weconstructed ideals C_i of the Iwasawa algebra, and proved that the ideals C_ibecome "upper bounds" of the higher Fitting ideals of the one and two variablep-adic unramified Iwasawa module X over an abelian extension field K_0 of animaginary quadratic field K. In this article, by using "non-arithmetic"specialization arguments, we prove that the ideals C_i also become "lowerbounds" of the higher Fitting ideals of X. In particular, we show that theideals C_i determine the pseudo-isomorphism class of X. Note that in thisarticle, we also treat the cases when the p-part of the equivariant Tamagawanumber conjecture (ETNC)_p is not proved yet.  In the cases when (ETNC)_p is proved, stronger results have already beenobtained by Burns, Kurihara and Sano: under the assumption of (ETNC)_p andcertain conditions on the character $\psi$ on the Galois group of K_0/K, theyhave given a complete description of the higher Fitting ideals of the\psi-component of X by using Rubin--Stark elements. In our article, we alsoprove that the $\psi$-part of C_i coincide with the ideals constructed byBurns, Kurihara and Sano in certain cases when (ETNC)_p is proved. As acorollary of this comparison results, we also deduce that the annihilator idealof the $\psi$-part of the maximal pseudo-null submodule of X coincides with theinitial Fitting ideal in certain situations.

On higher Fitting ideals of Iwasawa modules of ideal class groups over imaginary quadratic fields and Euler systems of elliptic units II