论文标题
以积极特征和galois表示的三角洲字符
Delta Characters in Positive Characteristic and Galois Representations
论文作者
论文摘要
在本文中，我们开发了$δ$ - 安德森模块的特征。考虑到任何Anderson模块$ e $（满足某些条件），使用$δ$ - 几何的理论，我们用hodge-pink结构构建了一个规范的$ z $ -isocrystal $ {\ mathbf {\ mathbf {h}_δ（e）} $。作为一个应用程序，我们表明，当$ e $是德林菲尔德模块时，我们构造的$ z $ -isocrystal $ {\ mathbf {h}_Δ（e）} $是差不多的，鉴于$Δ$ - 参数是非零。因此，Fontaine Foundator的同等特征类似物将局部shtuka关联，因此结晶$ z $ -ADIC GALOIS代表与$δ$ - 几何对象$ {\ MATHBF {h} h}_Δ（e）} $。众所周知，$ e $有一个天然的本地shtuka。对于Carlitz模块，我们表明与$ {\ Mathbf {h}_δ（e）} $相关的Galois表示确实是来自Tate模块的通常的代表。因此，本文进一步提出了一个问题，即在上述两个明显不同的Galois表示形式如何在任意等级的Drinfeld模块中相互比较。
In this article we develop the theory of $δ$-characters of Anderson modules. Given any Anderson module $E$ (satisfying certain conditions), using the theory of $δ$-geometry, we construct a canonical $z$-isocrystal ${\mathbf{H}_δ(E)}$ with a Hodge-Pink structure. As an application, we show that when $E$ is a Drinfeld module, our constructed $z$-isocrystal ${\mathbf{H}_δ(E)}$ is weakly admissible given that a $δ$-parameter is non-zero. Therefore the equal characteristic analogue of the Fontaine functor associates a local shtuka and hence a crystalline $z$-adic Galois representation to the $δ$-geometric object ${\mathbf{H}_δ(E)}$. It is also well known that there is a natural local shtuka attached to $E$. In the case of Carlitz modules, we show that the Galois representation associated to ${\mathbf{H}_δ(E)}$ is indeed the usual one coming from the Tate module. Hence this article further raises the question of how the above two apparently different Galois representations compare with each other for a Drinfeld module of arbitrary rank.
