On capitulations and pseudo-null submodules in certain ${\mathbb{Z}}_p^d$-extensions

Let $p$ be a prime number. By a result of Ozaki, the capitulations of ideals in ${\mathbb{Z}}_p$-extensions and the finite submodules of Iwasawa modules are closely related. In this article, we discuss this relationship in ${\mathbb{Z}}_p^d$-extensions.