论文标题
非交通性伊瓦川理论的主要猜想
A Main Conjecture in non-commutative Iwasawa theory
论文作者
论文摘要
我们在硫泽族的数字领域理论中制定了一个新的均值主要猜想，并研究其特性。这是针对任意的一维$ p $ -adic lie扩展的$ l_ \ infty/k $，其中包含Cyclotomic $ \ mathbb {z} _p $ - extension $ k_ \ infty $ k_ \ infty $。与该地区现有的猜想相反，不需要$ l_ \ infty/k $是阿贝里安（Abelian），否则$ l_ \ infty $是完全真实的。我们证明了基本上所有参数的主要猜想的独立性，并探索了其功能行为。此外，在很大程度上，这种新的猜想在很大程度上概括了现有的烧伤，库里亚拉（Kurihara），萨诺（Kurihara）和萨诺（Sano）以及里特（Ritter）和魏斯（Ritter and Weiss），这使我们能够在几种情况下推断出其有效性。
We formulate a new equivariant Main Conjecture in Iwasawa theory of number fields and study its properties. This is done for arbitrary one-dimensional $p$-adic Lie extensions $L_\infty/K$ containing the cyclotomic $\mathbb{Z}_p$-extension $K_\infty$ of the base field. As opposed to existing conjectures in the area, no requirement that $L_\infty/K$ be abelian or that $L_\infty$ be totally real is imposed. We prove the independence of the Main Conjecture of essentially all of its parameters and explore its functorial behaviour. It is furthermore shown that, to a large extent, this new conjecture generalises existing ones of Burns, Kurihara and Sano and Ritter and Weiss, which enables us to deduce its validity in several cases.
