Representations of Fundamental Groups of Algebraic Varieties / by Kang Zuo.

Format:

Book

Author/Creator:

Zuo, Kang, 1955- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1708.

Lecture Notes in Mathematics, 0075-8434 ; 1708

Language:

English

Subjects (All):

Geometry, Algebraic.

Mathematics.

Global analysis (Mathematics).

Algebraic topology.

Algebraic Geometry.

Applications of Mathematics.

Global Analysis and Analysis on Manifolds.

Algebraic Topology.

Local Subjects:

Algebraic Geometry.

Applications of Mathematics.

Global Analysis and Analysis on Manifolds.

Algebraic Topology.

Physical Description:

1 online resource (X, 135 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999.

System Details:

text file PDF

Summary:

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. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.

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...

Other Format:

Printed edition:

ISBN:

9783540484240

Access Restriction:

Restricted for use by site license.