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- W3100876364 abstract "For a CM-field $K$ and an odd prime number $p$, let $widetilde K'$ be a certain multiple $mathbb{Z}_p$-extension of $K$. In this paper, we study several basic properties of the unramified Iwasawa module $X_{widetilde K'}$ of $widetilde K'$ as a $mathbb{Z}_p[[{rm Gal}(widetilde K'/K)]]$-module. Our first main result is a description of the order of a Galois coinvariant of $X_{widetilde K'}$ in terms of the characteristic power series of the unramified Iwasawa module of the cyclotomic $mathbb{Z}_p$-extension of $K$ under a certain assumption on the splitting of primes above $p$. Second one is that if $K$ is an imaginary quadratic field and $p$ does not split in $K$, we give a necessary and sufficient condition for which $X_{widetilde K}$ is $mathbb{Z}_p[[{rm Gal}(widetilde K/K)]]$-cyclic under several assumptions on the Iwasawa $lambda$-invariant and the ideal class group of $K$, where $widetilde K$ is the $mathbb{Z}_p^2$-extension of $K$." @default.
- W3100876364 created "2020-11-23" @default.
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- W3100876364 date "2020-11-11" @default.
- W3100876364 modified "2023-10-16" @default.
- W3100876364 title "Galois coinvariants of the unramified Iwasawa modules of multiple $$mathbb {Z}_p$$-extensions" @default.
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- W3100876364 doi "https://doi.org/10.1007/s40316-020-00150-6" @default.
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