Representations of Fundamental Groups of Algebraic Varieties
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. T...
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| Format: | Electronic eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
1999.
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| Edition: | 1st ed. 1999. |
| Series: | Lecture Notes in Mathematics,
1708 |
| Subjects: | |
| Online Access: | Full Text via HEAL-Link |
Table of Contents:
- Introduction
- Preliminaries
- Review of Algebraic groups over arbitrary fields
- Representations of phi1 and the Moduli space
- p-adic norm on a vector space and Bruhat-Tits buildings
- Harmonic metric on flat vector bundle
- Pluriharmonic map of finite energy
- Pluriharmonic maps of possibly infinite energy but with controlled growth at infinity
- Non-abelian Hodge theory, factorization theorems for non rigid or p-adic unbound representations
- Higgs bundles for archimedean representations and equivariant holomorphic 1-forms for p-adic representations
- Albanese maps and a Lefschetz type theorem for holomorphic 1-forms
- Factorizations for nonrigid representations into almost simple complex algebraic groups
- Factorization for p-adic unbounded representations into almost simple p-adic algebraic groups
- Simpson's construction of families on non rigid representations
- Shavarevich maps for representations of phi1, Kodaira dimension and Chern-hyperbolicity of Shavarevich varieties...
