论文标题
弱格林伯格对假想二次领域的普遍猜想
Weak Greenberg's generalized conjecture for imaginary quadratic fields
论文作者
论文摘要
让$ p $是一个奇数的质数，$ k $是一个虚构的二次领域，其中$ p $拆分。在本文中，我们考虑了格林伯格对$ p $和$ k $的广义猜想的一种薄弱形式，该猜想指出，最大多$ \ mathbb {z} _p $ extension _ $ k $的非平凡的iwasawa模块具有非平凡的pseudo-null-null subpsodule。我们证明了$ p $和$ k $的这种猜想，假设是iWasawa $λ$ - 以某种$ \ mathbb {z} _p $ - $ k $ vanish的有限延伸而变化的一定$ \ mathbb {z} _p $ - vanishes的特征与iwasawa $ $ k $ k $ k $ k $ k的特征性的理想{无方形的发电机。
Let $p$ be an odd prime number and $k$ an imaginary quadratic field in which $p$ splits. In this paper, we consider a weak form of Greenberg's generalized conjecture for $p$ and $k$, which states that the non-trivial Iwasawa module of the maximal multiple $\mathbb{Z}_p$-extension field over $k$ has a non-trivial pseudo-null submodule. We prove this conjecture for $p$ and $k$ under the assumption that the Iwasawa $λ$-invariant for a certain $\mathbb{Z}_p$-extension over a finite abelian extension of $k$ vanishes and that the characteristic ideal of the Iwasawa module associated to the cyclotomic $\mathbb{Z}_p$-extension over $k$ has a square-free generator.
