On pseudo-isomorphism classes of tamely ramified Iwasawa modules over imaginary quadratic fields
Volume 180 / 2017
Acta Arithmetica 180 (2017), 171-182 MSC: Primary 11R23; Secondary 11R29. DOI: 10.4064/aa170127-27-4 Published online: 30 August 2017
We determine, under some conditions, the pseudo-isomorphism classes of the tamely ramified Iwasawa modules for the $\mathbb Z_p^2$-extension of an imaginary quadratic field. Moreover, we deduce a result for $\mathbb Z_p$-extensions. This work is motivated by a study of Itoh–Mizusawa–Ozaki which essentially determines the pseudo-isomorphism classes of the tamely ramified Iwasawa modules for the cyclotomic $\mathbb Z_p$-extension of the field $\mathbb Q$ of rational numbers.