论文标题
Hodge-Iwasawa理论i
Hodge-Iwasawa Theory I
论文作者
论文摘要
在本文中，我们将同时建立Kedlaya-Pottharst提出的相对Iwasawa理论的同时概括，以及Kedlaya-liu之后的相对$ p $ -Adic Hodge理论。我们称这种hodge-iwasawa理论是从某种意义上说，人们可以将理论应用于家庭中的非共同伊瓦萨岛的共同体和非共同的伊瓦苏瓦理论，同时也可以利用该理论来研究典型的本地系统的变形理论，以等效的$ $ $ $ $ $ $ - 阿德维斯的概述，以$ $ $ $ $ $ $调的方式来看，以$ $ - 阿德的构建，并以此为代表。福卡 - 卡托。我们密切关注Kedlaya-liu的方法，以研究相应的变形版本和周期或骨的相应变形版本。
In this paper, we are going to establish a simultaneous generalization of the relative Iwasawa theory proposed by Kedlaya-Pottharst and the relative $p$-adic Hodge theory after Kedlaya-Liu. We call this Hodge-Iwasawa theory in the sense that one could apply the theory to study noncommutative Iwasawa cohomology and noncommutative Iwasawa theories in families and meanwhile one could apply the theory to study the deformation theory of étale local systems or families of representations of fundamental groups or the equivariant constructible $p$-adic sheaves, with more sophisticated point of view coming from Kato, Fukaya-Kato. We follow closely the approach of Kedlaya-Liu to study the corresponding modules and sheaves over the corresponding deformed version of the period rings and period sheaves.
