A remark on Greenberg's generalized conjecture for imaginary $S_3$-extensions of $\mathbb{Q}$

arXiv (Cornell University)（2023）

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Abstract

Let $K/ \mathbb{Q}$ be an imaginary $S_3$-extension, and $p$ a prime number which splits into exactly three primes in $K$. We give a sufficient condition for the validity of Greenberg's generalized conjecture for $K$ and $p$.

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Key words

generalized conjecture,greenberg

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