论文标题
在Euler系统的功能方程式上
On functional equations of Euler systems
论文作者
论文摘要
我们在Euler系统之间建立了与$ p $ -ADIC表示$ t $和其Kummer dual dual $ t^*（1）$相关的Euler系统之间的精确关系。在适当专业化了这一总体结果后，我们能够在完全真实的字段$ k $上推断出等级$ [k：\ mathbb {q}] $的欧拉系统的存在，这两者都介绍了$ k $ $ k $的dedekind Zeta Zeta函数的价值，即使是$ k $，甚至还确定了$ \ materb的$ \ selmer ob blybb y Mathb的oblbb的oblbb的理想的范围。 $ k $。反过来，这种构建促使制定了Coleman-Ihara公式的精确猜想概括，我们为这种猜想提供了支持的证据。
We establish precise relations between Euler systems that are respectively associated to a $p$-adic representation $T$ and to its Kummer dual $T^*(1)$. Upon appropriate specialization of this general result, we are able to deduce the existence of an Euler system of rank $[K:\mathbb{Q}]$ over a totally real field $K$ that both interpolates the values of the Dedekind zeta function of $K$ at all positive even integers and also determines all higher Fitting ideals of the Selmer groups of $\mathbb{G}_m$ over abelian extensions of $K$. This construction in turn motivates the formulation of a precise conjectural generalization of the Coleman-Ihara formula and we provide supporting evidence for this conjecture.
