On higher special elements of p-adic representations
On higher special elements of p-adic representations
复制标题
关于 p 进表示的高级特殊元素
DOI：
10.1093/imrn/rnz378
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发表时间：
2020
影响因子：
1
通讯作者：
Kwok-Wing Tsoi
中科院分区：
文献类型：
--
作者：
David Burns;Takamichi Sano;Kwok-Wing Tsoi
作为“高阶欧拉系统”概念的自然推广，我们发展了一个关于-adic表示的伽罗瓦上同调的外幂双线性中的“高阶特殊元”的理论。我们发现，特别是，这些元素编码的详细信息的伽罗瓦上同调组的结构和相关的家庭的同余涉及自然高度配对上同调。作为第一个具体的应用程序的方法，我们用它来完善，并扩展，各种现有的结果和aptures关于的Dirichlet级数的导数的值。
As a natural generalisation of the notion of “higher rank Euler system”, we develop a theory of “higher special elements” in the exterior power biduals of the Galois cohomology of-adic representations. We show, in particular, that such elements encode detailed information about the structure of Galois cohomology groups and are related by families of congruences involving natural height pairings on cohomology. As a first concrete application of the approach, we use it to refine, and extend, a variety of existing results and conjectures concerning the values of derivatives of Dirichlet-series.