论文标题
简单的galois变形函子
Simplicial Galois Deformation Functors
论文作者
论文摘要
在Galatius和Venkatesh的最新工作中，作者表明了研究Galois变形函子的简单概括的重要性。他们在简单的通用变形环$ r $之间建立了一个精确的联系，即具有当地条件）和派生的Hecke代数。在这里，我们专注于他们研究的代数部分，我们在两个方向上完成。首先，我们介绍了简单伪符号的概念，并证明了简单伪字符的（派生）变形函数与简单的Galois表示的（派生的）变形函数。其次，我们定义了简单变形函子的相对旋转复合物，在普通情况下，我们将其与普通Galois Cochains的相对复合物相关联。最后，我们回想起如何使用后者将$ r $的基本组与普通的双伴侣组联系在一起，这是通过在Galatius-venkatesh中引入的同构和在Tilouine-Urban中更大的一般性研究的同构的。
In a recent work of Galatius and Venkatesh, the authors showed the importance of studying simplicial generalizations of Galois deformation functors. They established a precise link between the simplicial universal deformation ring $R$ prorepresenting such a deformation problem (with local conditions) and a derived Hecke algebra. Here we focus on the algebraic part of their study which we complete in two directions. First, we introduce the notion of simplicial pseudo-characters and prove relations between the (derived) deformation functors of simplicial pseudo-characters and that of simplicial Galois representations. Secondly, we define the relative cotangent complex of a simplicial deformation functor and, in the ordinary case, we relate it to the relative complex of ordinary Galois cochains. Finally, we recall how the latter can be used to relate the fundamental group of $R$ to the ordinary dual adjoint Selmer group, by a homomorphism already introduced in Galatius-Venkatesh and studied in greater generality in Tilouine-Urban.
