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Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization
- C. Simpson
- Mathematics
- 13 January 1988
The fundamental group is one of the most basic topological invariants of a space. The aim of this paper is to present a method of constructing representations of fundamental groups in complex…
Higgs bundles and local systems
- C. Simpson
- Mathematics
- 1 December 1992
© Publications mathématiques de l’I.H.É.S., 1992, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » ( http://www.…
Moduli of representations of the fundamental group of a smooth projective variety I
- C. Simpson
- Mathematics
- 1 December 1994
© Publications mathématiques de l’I.H.É.S., 1994, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
Harmonic bundles on noncompact curves
- C. Simpson
- Mathematics
- 1 September 1990
The purpose of this paper is to extend the correspondence between Higgs bundles and local systems [2,5,6,7, 13, 17, 19,20,21] to the case when X is a noncom pact algebraic curve. The basic result is…
Moduli of representations of the fundamental group of a smooth projective variety. II
- C. Simpson
- Mathematics
- 1994
© Publications mathématiques de l’I.H.É.S., 1994, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
Subspaces of moduli spaces of rank one local systems
- C. Simpson
- Mathematics
- 1993
Suppose X is a smooth projective variety. The moduli space M (X) of rank one local systems on X has three different structures of complex algebraic group (Betti, de Rham, and Dolbeault). A subgroup…
Mixed twistor structures
- C. Simpson
- Mathematics
- 5 May 1997
The purpose of this paper is to introduce the notion of mixed twistor structure, a generalization of the notion of mixed Hodge structure. The utility of this notion is to make possible a theory of…
$B$-structures on $G$-bundles and local triviality
- V. Drinfeld, C. Simpson
- Mathematics
- 1995
1. Let G be a split reductive group scheme over Z (recall that for any algebraically closed field k there is a bijection G → G ⊗ k between isomorphism classes of such group schemes and isomorphism…
The Hodge filtration on nonabelian cohomology
- C. Simpson
- Mathematics
- 4 April 1996
This is partly a survey article on nonabelian Hodge theory, but we also give proofs of results that have only been announced elsewhere. In the introduction we discuss a wide range of recent work on…
Homotopy types of strict 3-groupoids
- C. Simpson
- Mathematics
- 9 October 1998
We look at strict $n$-groupoids and show that if $\Re$ is any realization functor from the category of strict $n$-groupoids to the category of spaces satisfying a minimal property of compatibility…
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