For an algebraic number field K and a prime number p, let K̃/K be the maximal multiple ℤp-extension. Greenberg’s generalized conjecture (GGC) predicts that the Galois group of the maximal unramified abelian pro-p extension of K̃ is pseudo-null over the completed group ring ℤp[[Gal(K̃/K)]]. We show that GGC holds for some imaginary quartic fields containing imaginary quadratic fields and some prime numbers.

中文翻译：

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关于格林伯格关于假想四次场的广义猜想

对于代数域ķ和一个素数p， 让ķ̃/ķ是最大倍数ℤp-延期。格林伯格的广义猜想 (GGC) 预测最大无分支阿贝尔投影的伽罗瓦群p的扩展ķ̃在已完成的群环上为伪空ℤp[[加尔(ķ̃/ķ)]]. 我们证明 GGC 适用于一些包含虚二次域和一些素数的虚四次域。