论文标题
关于higgs-de rham流量的注释
A note on Higgs-de Rham flows of level zero
论文作者
论文摘要
Higgs-de Rham流的概念是由Lan-Sheng-Zuo引入的，作为复杂的nonabelian Hodge理论中Yang-Mills-Higgs流的类似物。在此简短的说明中，我们研究了该理论的一小部分，并研究了零级的Higgs-De Rham流。我们改善了零级HIGGS-DE RHAM流（适用于一般级别）的原始定义，并在积极特征中建立了此类对象和基本组的某些代表之间的Hitchin-Simpson-type对应关系，这概括了Katz的经典结果。我们比较对应关系中两个方面的变形理论，并将galois的作用转化为在有限场上定义的代数品种的几何基本基团到Higgs侧的几何基本组。
The notion of Higgs-de Rham flows was introduced by Lan-Sheng-Zuo, as an analogue of Yang-Mills-Higgs flows in the complex nonabelian Hodge theory. In this short note we investigate a small part of this theory, and study those Higgs-de Rham flows which are of level zero. We improve the original definition of level-zero Higgs-de Rham flows (which works for general levels), and establish a Hitchin-Simpson-type correspondence between such objects and certain representations of fundamental groups in positive characteristic, which generalizes the classical results of Katz. We compare the deformation theories of two sides in the correspondence, and translate the Galois action on the geometric fundamental groups of algebraic varieties defined over finite fields into the Higgs side.
