论文标题
球形品种和非平民阶级家族
Spherical varieties and non-ordinary families of cohomology classes
论文作者
论文摘要
我们为与还原群的球形对相关的本地对称空间的共同体学中的非常见$ p $ - 亚法家庭构建。在典型的情况下，我们展示了如何将这些类别映射到Galois的共同体中。本文开发的方法可用于提供$ P $ - 美国欧拉系统家庭和$ p $ adic $ l $ functions的新结构。例如，我们展示了本文的构造如何用于构建与非常见的Siegel模块化形式相关的规范兼容类，从而概括了由Loeffler-skinner-Skinner-shibes构建的Lemma--Flach Euler系统的$ P $。
We give a construction of non-ordinary $p$-adic families of classes in the cohomology of locally symmetric spaces associated to spherical pairs of reductive groups. In the étale case, we show how to map these classes into Galois cohomology. The methods developed in this paper can be used to give new constructions of $p$-adic families of Euler systems and $p$-adic $L$-functions. As an example, we show how the constructions of this paper can be used to construct norm-compatible classes associated to non-ordinary Siegel modular forms, generalising $p$-part of the Lemma--Flach Euler system constructed by Loeffler--Skinner--Zerbes.
