论文标题
关于欧拉系统模块的结构
On the structure of the module of Euler systems for a $p$-adic representation
论文作者
论文摘要
我们调查了一个关于欧拉系统模块的结构，以$ p $ - ad的代表制度研究了一个伯恩斯和萨诺的问题。假设Leopoldt的猜想较弱，并且消失了自然iWasawa模块的$ $ $ invariants，我们获得了用于研究该模块的Euler Systems的Iwasawa理论分类标准。该标准与科尔曼（Coleman）对圆形分布的猜想一起，使我们提出了上述问题的改进，我们为此提供了强有力且无条件的证据。在许多有趣的情况下，在数字字段上，我们在许多有趣的情况下，在许多有趣的情况下，我们在肯定的情况下回答了这个问题。由于这些结果，我们在考虑情况下对欧拉系统的完整集合的结构进行了明确描述。
We investigate a question of Burns and Sano concerning the structure of the module of Euler systems for a general $p$-adic representation. Assuming the weak Leopoldt conjecture, and the vanishing of $μ$-invariants of natural Iwasawa modules, we obtain an Iwasawa-theoretic classification criterion for Euler systems which can be used to study this module. This criterion, taken together with Coleman's conjecture on circular distributions, leads us to pose a refinement of the aforementioned question for which we provide strong, and unconditional, evidence. We furthermore answer this question in the affirmative in many interesting cases in the setting of the multiplicative group over number fields. As a consequence of these results, we derive explicit descriptions of the structure of the full collection of Euler systems for the situations in consideration.
