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arXiv · 2001.11768

On Greenberg's generalized conjecture for imaginary quartic fields

Naoya Takahashi
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Abstract

For an algebraic number field $K$ and a prime number $p$, let $\widetilde{K}/K$ be the maximal multiple $\mathbb{Z}_p$-extension. Greenberg's generalized conjecture (GGC) predicts that the Galois group of the maximal unramified abelian pro-$p$ extension of $\widetilde{K}$ is pseudo-null over the completed group ring $\mathbb{Z}_p[\![\mathop{\mathrm{Gal}}\nolimits(\widetilde{K}/K)]\!]$. We show that GGC holds for some imaginary quartic fields containing imaginary quadratic fields and some prime numbers.

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Naoya Takahashi. 2020-01-31. On Greenberg's generalized conjecture for imaginary quartic fields. https://arxiv.org/abs/2001.11768

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