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Representations of Fundamental Groups of Algebraic Varieties : Lecture Notes in Mathematics - K Zuo

Representations of Fundamental Groups of Algebraic Varieties

Lecture Notes in Mathematics

By: K Zuo

Paperback Published: February 2000
ISBN: 9783540663126
Number Of Pages: 135

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Using harmonic maps, non-linear PDE & techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups & algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry & 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.

Introductionp. 1
Preliminariesp. 10
Review of Algebraic groups over arbitrary fieldsp. 10
Representations of fundamental groups and Moduli spacesp. 12
p-adic norm on a vector space and Bruhat-Tits buildingsp. 20
Harmonic metrics on flat vector bundlesp. 25
Pluriharmonic maps of finite energyp. 25
Pluriharmonic maps of possibly infinite energy but with con- trolled growth at infinityp. 41
Non-abelian Hodge theory, factorization theorems for non rigid or p-adic unbounded representationsp. 52
Higgs bundles for archimedean representations and equivari- ant holomorphic 1-forms for p-adic representationsp. 52
Albanese maps and a Lefschetz type theorem for holomorphic 1-formsp. 63
Factorizations for nonrigid representations into almost simple complex algebraic groupsp. 83
Factorizations for p-adic unbounded representations into al- most simple p-adic algebraic groupsp. 97
Simpson's construction of families of nonrigid representationsp. 101
Shafarevich maps for representations of fundamental groups, Kodaira dimension and Chern-hyperbolicity of Shafarevich varietiesp. 104
Shafarevich maps and general discussionsp. 104
Constructing automorphic forms via equivariant pluriharmonic maps into Bruhat-Tits buildingp. 111
Kodaira dimension and Chern-hyperbolicity of Shafarevich va- rietiesp. 113
A finiteness property of representations of fundamental groups of algebraic surfaces, which contain configurations of rational curvesp. 119
Referencep. 125
Indexp. 133
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540663126
ISBN-10: 3540663126
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 135
Published: February 2000
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.84
Weight (kg): 0.22

Earn 138 Qantas Points
on this Book