论文标题
Split Prime $ p = 2 $的假想二次字段的主要猜想
The Main Conjecture for Imaginary quadratic fields for the split prime $p=2$
论文作者
论文摘要
令$ \ mathbb {k} $为一个虚构的二次字段，以便$ 2 $分为两个Primes $ \ Mathfrak {p} $和$ \ bar {\ mathfrak {p}} $。令$ \ mathbb {k} _ {\ infty} $为unique $ \ mathbb {z} _2 $ - extension $ \ mathbb {k {k} $在$ \ mathfrak {p} $之外未经密码。令$ \ mathfrak {f} $是与$ \ Mathfrak {p} $和$ \ Mathbb {l} $的理想级别，是$ \ Mathbb {k} $的任意扩展，其中包含在Ray Class Field $ \ Mathbb {k}（k}（k}（\ Mathfrak）中，令$ \ mathbb {l} _ {\ infty} = \ mathbb {k} _ {\ infty} \ mathbb {l} $，让$ \ mathbb {m mathbb {m} $是最大$ p $ p $ -Abelian，$ p $ -Abelian，$ \ m m iathfrak {p} $ \ mathbb {l} _ {\ infty} $。我们设置$ x = gal（\ mathbb {m}/\ mathbb {l} _ {\ infty}）$。在本文中，我们证明了模块$ x $的iWasawa主要猜想。
Let $\mathbb{K}$ be an imaginary quadratic field such that $2$ splits into two primes $\mathfrak{p}$ and $\bar{\mathfrak{p}}$. Let $\mathbb{K}_{\infty}$ be the unique $\mathbb{Z}_2$-extension of $\mathbb{K}$ unramified outside $\mathfrak{p}$. Let $\mathfrak{f}$ be an ideal coprime to $\mathfrak{p}$ and $\mathbb{L}$ be an arbitrary extension of $\mathbb{K}$ contained in the ray class field $\mathbb{K}(\mathfrak{p}^2\mathfrak{f})$. Let $\mathbb{L}_{\infty}=\mathbb{K}_{\infty}\mathbb{L}$ and let $\mathbb{M}$ be the maximal $p$-abelian, $\mathfrak{p}$-ramified extension of $\mathbb{L}_{\infty}$. We set $X=Gal(\mathbb{M}/\mathbb{L}_{\infty})$. In this paper we prove the Iwasawa main conjecture for the module $X$.
