A consequence of Greenberg's generalized conjecture on Iwasawa invariants of -extensions

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• 作者：Takenori Kataoka ^{tkataoka@ms.u-tokyo.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Iwasawa theory ; Greenberg's generalized conjecture ; Iwasawa invariants
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：Complete
• 页码：200-233
• 全文大小：593 K

文摘

For a prime number p and a number field k  , let $\tilde{k}$ be the compositum of all 622465e6e1c" title="Click to view the MathML source">Z_p${\mathbb{Z}}_p$-extensions of k  . Greenberg's Generalized Conjecture (GGC) claims the pseudo-nullity of the unramified Iwasawa module $X(\tilde{k})$ of $\tilde{k}$. It is known that, when k   is an imaginary quadratic field, GGC has a consequence on the Iwasawa invariants associated to 622465e6e1c" title="Click to view the MathML source">Z_p${\mathbb{Z}}_p$-extensions of k. In this paper, we partially generalize it to arbitrary number fields k.