论文标题
关于格林伯格的普遍猜想
On Greenberg's generalized conjecture for imaginary quartic fields
论文作者
论文摘要
对于代数数字字段$ k $和prime数字$ p $，令$ \ widetilde {k}/k $为最大$ \ mathbb {z} _p $ - extension。格林伯格的广义猜想（GGC）预测，最大未受到的Abelian Pro- $ p $ $ \ widetilde {k} $的Galois组是完整的组环上的Pseudo-null $ \ mathbb {z} _p [\！[\ mathop {\ mathrm {gal}}} \ nolimits（\ widetilde {k}/k）/k）] \！] $。我们表明，GGC适用于一些想象中的四分之一的四分之一字段，其中包含想象中的二次字段和一些质数。
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.
