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On the classification of rank-two representations of quasiprojective fundamental groups

Part of: Compact analytic spaces Lie groups Variational problems in infinite-dimensional spaces Families, fibrations

Published online by Cambridge University Press:  01 September 2008

Kevin Corlette  and
Carlos Simpson
Kevin Corlette
Affiliation:
University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA (email: [email protected])
Carlos Simpson
Affiliation:
CNRS, Laboratoire J. A. Dieudonné, UMR 6621, Université de Nice-Sophia Antipolis, 06108 Nice, Cedex 2, France (email: [email protected])
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Abstract

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Suppose that X is a smooth quasiprojective variety over ℂ and ρ:π1(X,x)→SL(2,ℂ) is a Zariski-dense representation with quasiunipotent monodromy at infinity. Then ρ factors through a map X→Y with Y either a Deligne–Mumford (DM) curve or a Shimura modular stack.

Keywords

fundamental grouprepresentationharmonic maptreeDeligne–Mumford stackShimura variety

MSC classification

Secondary: 58E20: Harmonic maps , etc. 14D07: Variation of Hodge structures 22E40: Discrete subgroups of Lie groups 32J27: Compact Kähler manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 5 , September 2008 , pp. 1271 - 1331
Copyright
Copyright © Foundation Compositio Mathematica 2008