Moduli of representations of the fundamental group of a smooth projective variety I
Publications Mathématiques de l'IHÉS, Volume 79 (1994), pp. 47-129.
@article{PMIHES_1994__79__47_0,
     author = {Simpson, Carlos T.},
     title = {Moduli of representations of the fundamental group of a smooth projective variety {I}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {47--129},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {79},
     year = {1994},
     mrnumber = {1307297},
     zbl = {0891.14005},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1994__79__47_0/}
}
TY  - JOUR
AU  - Simpson, Carlos T.
TI  - Moduli of representations of the fundamental group of a smooth projective variety I
JO  - Publications Mathématiques de l'IHÉS
PY  - 1994
SP  - 47
EP  - 129
VL  - 79
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1994__79__47_0/
LA  - en
ID  - PMIHES_1994__79__47_0
ER  - 
%0 Journal Article
%A Simpson, Carlos T.
%T Moduli of representations of the fundamental group of a smooth projective variety I
%J Publications Mathématiques de l'IHÉS
%D 1994
%P 47-129
%V 79
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1994__79__47_0/
%G en
%F PMIHES_1994__79__47_0
Simpson, Carlos T. Moduli of representations of the fundamental group of a smooth projective variety I. Publications Mathématiques de l'IHÉS, Volume 79 (1994), pp. 47-129. http://www.numdam.org/item/PMIHES_1994__79__47_0/

[Ar] M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S., 36 (1969), 23-58. | EuDML | Numdam | MR | Zbl

[Be] J. Bernstein, Course on D-modules, Harvard, 1983-1984.

[BT] A. Borel, J. Tits, Eléments unipotents et sous-groupes paraboliques de groupes réductifs I, Invent. Math., 12 (1971), 95-104. | EuDML | MR | Zbl

[Co] K. Corlette, Flat G-bundles with canonical metrics, J. Diff. Geom., 28 (1988), 361-382. | MR | Zbl

[De1] P. Deligne, Equations différentielles à points singuliers réguliers, Lect. Notes in Math., 163, Springer, New York (1970). | MR | Zbl

[De2] P. Deligne, Letter.

[DM] P. Deligne and J. Milne, Tannakian categories, In Lect. Notes in Math., 900, Springer (1982), 101-228. | MR | Zbl

[Do1] S. K. Donaldson, Anti self dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. (3), 50 (1985), 1-26. | MR | Zbl

[Do2] S. K. Donaldson, Infinite determinants, stable bundles, and curvature, Duke Math. J., 54 (1987), 231-247. | MR | Zbl

[Do3] S. K. Donaldson, Twisted harmonic maps and self-duality equations, Proc. London Math. Soc., 55 (1987), 127-131. | MR | Zbl

[Gi] D. Gieseker, On the moduli of vector bundles on an algebraic surface, Ann. of Math., 106 (1977), 45-60. | MR | Zbl

[GM] W. Goldman and J. Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Publ. Math. I.H.E.S., 67 (1988), 43-96. | Numdam | MR | Zbl

[Gr1] A. Grothendieck, Eléments de géométrie algébrique, Several volumes in Publ. Math. I.H.E.S. | Numdam | Zbl

[Gr2] A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique, IV : Les schémas de Hilbert, Sém. Bourbaki, Exposé 221, volume 1960-1961. | Numdam | Zbl

[Gr3] A. Grothendieck, Crystals and the De Rham cohomology of schemes, Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam (1968). | MR | Zbl

[GS] V. Guillemin, S. Sternberg, Birational equivalence in symplectic geometry, Invent. Math., 97 (1989), 485-522. | MR | Zbl

[Ha] R. Hartshorne, Algebraic Geometry, Springer, New York (1977). | MR | Zbl

[Hi1] N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 59-126. | MR | Zbl

[Hi2] N. J. Hitchin, Stable bundles and integrable systems, Duke Math. J., 54 (1987), 91-114. | MR | Zbl

[KN] G. Kempf, L. Ness, On the lengths of vectors in representation spaces, Lect. Notes in Math., 732, Springer, Heidelberg (1982), 233-243. | MR | Zbl

[Ki] F. Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry, Princeton Univ. Press, Princeton (1984). | MR | Zbl

[Le] J. Le Potier, Fibrés de Higgs et systèmes locaux, Séminaire Bourbaki 737 (1991). | Numdam | MR | Zbl

[Lu] D. Luna, Slices étales, Bull. Soc. Math. France, Mémoire 33 (1973), 81-105. | Numdam | MR | Zbl

[Ma1] M. Maruyama, Moduli of stable sheaves, I : J. Math. Kyoto Univ., 17-1 (1977), 91-126 ; II : Ibid., 18-3 (1978), 557-614. | MR | Zbl

[Ma2] M. Maruyama, On boundedness of families of torsion free sheaves, J. Math. Kyoto Univ., 21-4 (1981), 673-701. | MR | Zbl

[Mt] Matsushima, See reference in Geometric Invariant Theory.

[MR1] V. B. Mehta and A. Ramanathan, Semistable sheaves on projective varieties and their restriction to curves, Math. Ann., 258 (1982), 213-224. | MR | Zbl

[MR2] V. B. Mehta and A. Ramanathan, Restriction of stable sheaves and representations of the fundamental group, Invent. Math., 77 (1984), 163-172. | MR | Zbl

[Mo] V. V. Morozov, Proof of the regularity theorem (Russian), Usp. M. Nauk., XI (1956), 191-194. | MR | Zbl

[Mu] D. Mumford, Geometric Invariant Theory, Springer Verlag, New York (1965). | MR | Zbl

[NS] M. S. Narasimhan and C. S. Seshadri, Stable and unitary bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-564. | MR | Zbl

[Ni1] N. Nitsure, Moduli space of semistable pairs on a curve, Proc. London Math. Soc., 62 (1991), 275-300. | MR | Zbl

[Ni2] N. Nitsure, Moduli of semi-stable logarithmic connections, Jour. Amer. Math. Soc., 6 (1993), 597-610. | MR | Zbl

[No] M. V. Nori, On the representations of the fundamental group, Compositio Math., 33 (1976), 29-41. | Numdam | MR | Zbl

[Ox] W. M. Oxbury, Spectral curves of vector bundle endomorphisms, preprint, Kyoto University (1988).

[Ru] W. Rudin, Real and Complex Analysis, Mac Graw-Hill, New York (1974). | MR | Zbl

[Sa] N. Saavedra Rivano, Catégories tannakiennes, Lect. Notes in Math., 265 Springer, (1972). | MR | Zbl

[Se1] C. S. Seshadri, Space of unitary vector bundles on a compact Riemann surface, Ann. of Math., 85 (1967), 303-336. | MR | Zbl

[Se2] C. S. Seshadri, Mumford's conjecture for GL(2) and applications, Bombay Colloquium, Oxford University Press (1968), 347-371. | MR | Zbl

[Si1] C. Simpson, Yang-Mills theory and uniformization, Lett. Math. Phys., 14 (1987), 371-377. | MR | Zbl

[Si2] C. Simpson, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, Journal of the A.M.S., 1 (1988), 867-918. | MR | Zbl

[Si3] C. Simpson, Nonabelian Hodge theory, International Congress of Mathematicians, Kyoto 1990, Proceedings, Springer, Tokyo (1991), 747-756. | MR | Zbl

[Si4] C. Simpson, A lower bound for the monodromy of ordinary differential equations, Analytic and Algebraic Geometry, Tokyo 1990, Proceedings, Springer, Tokyo (1991), 198-230. | MR | Zbl

[Si5] C. Simpson, Higgs bundles and local systems, Publ. Math. I.H.E.S., 75 (1992), 5-95. | Numdam | MR | Zbl

[Uh] K. K. Uhlenbeck, Connections with Lp bounds on curvature, Commun. Math. Phys., 83 (1982), 31-42. | MR | Zbl

[UY] K. K. Uhlenbeck and S. T. Yau, On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure and Appl. Math., 39-S (1986), 257-293. | MR | Zbl