A note on Higgs-de Rham flows of level zero

• 作者: Mao Sheng Jilong Tong
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（2）
• 所属期刊栏目: Articles
• 页码范围: 307-330
• 页数: 24页
• 语种: 英文

摘要

The notion of Higgs-de Rham flows was introduced by Lan et al.(2019),as an analogue of Yang-Mills-Higgs flows in the complex nonabelian Hodge theory.In this paper 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 corre-spondence between such objects and certain representations of fundamental groups in positive characteristic,which generalizes a classical results of Katz(1973).We compare the deformation theories of two sides in the cor-respondence,and translate the Galois action on the geometric fundamental groups of algebraic varieties defined over finite fields into the Higgs side.