ISBN: 3-540-66312-6
TITLE: Representations of Fundamental Groups of Algebraic Varieties
AUTHOR: Zuo, Kang
TOC:
1 Introduction 1
2 Preliminaries 10
2.1 Review of Algebraic groups over arbitrary fields 10
2.2 Representations of fundamental groups and Moduli spaces 12
2.3 padic norm on a vector space and Bruhat-Tits buildings 20
3 Harmonic metrics on flat vector bundles 25
3.1 Pluriharmonic maps of finite energy 25
3.2 Pluriharmonic maps of possibly infinite energy but with controlled growth at infinity 41
4 Non-abelian Hodge theory, factorization theorems for non rigid or p-adic unbounded representations 52
4.1 Higgs bundles for archimedean representations and equivariant holomorphic 1-forms for padic representations 52
4.2 Albanese maps and a Lefschetz type theorem for holomorphic 1-forms 63
4.3 Factorizations for nonrigid representations into almost simple complex algebraic groups 83
4.4 Factorizations for p-adic unbounded representations into al- most simple p-adic algebraic groups 97
4.5 Simpson's construction of families of nonrigid representations 101
5 Shafarevich maps for representations of fundamental groups, Kodaira dimension and Chern-hyperbolicity of Shafarevich varieties 104
5.1 Shafarevich maps and general discussions 104
5.2 Constructing automorphic forms via equivariant pluriharmonic maps into Bruhat-Tits building 111
5.3 Kodaira dimension and Chern-hyperbolicity of Shafarevich varieties 113
5.4 A finiteness property of representations of fundamental groups of algebraic surfaces, which contain configurations of rational curves 119
Reference 125
Index 133
END