Higgs bundles and local systems

Simpson, Carlos T. 

Publications Mathématiques de l'IHÉS, Tome 75 (1992), pp. 5-95.

Bibliographie

[1] L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc., 43, no. 3 (1938), 359-364. | Zbl | MR | JFM

[2] H. Bass, Groups of integral representation type, Pacific J. of Math., 86 (1980), 15-51. | Zbl | MR

[3] A. Borel and W. Casselman, L2-cohomology of locally symmetric manifolds of finite volume, Duke Math. J., 50 (1983), 625-647. | Zbl | MR

[4] J. A. Carlson and D. Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces, Publ. Math. I.H.E.S., 69 (1989), 173-201. | Zbl | MR | mathdoc-id

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

[6] K. Corlette, Rigid representations of Kählerian fundamental groups, J. Diff. Geom., 33 (1991), 239-252. | Zbl | MR

[7] P. Deligne, letter to J.-P. Serre (1968).

[8] P. Deligne, Un théorème de finitude pour la monodromie, Discrete Groups in Geometry and Analysis, Birkhauser (1987), 1-19. | Zbl | MR

[9] P. Deligne, La conjecture de Weil pour les surfaces K3, Invent. Math., 15 (1972), 206-222. | Zbl | MR

[10] P. Deligne, Theorie de Hodge, II, Publ. Math. I.H.E.S., 40 (1971), 5-58. | Zbl | MR | mathdoc-id

[11] P. Deligne, Travaux de Shimura, Séminaire Bourbaki, Lect. Notes in Math., 244 (1971), 123-165. | Zbl | MR | mathdoc-id

[12] P. Deligne, P. Griffiths, J. Morgan and D. Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math., 29 (1975), 245-274. | Zbl | MR

[13] P. Deligne, J. S. Milne, A. Ogus and K. Shih, Hodge Cycles, Motives, and Shimura Varieties, Lect. Notes in Math., 900 (1982), Heidelberg, Springer. | Zbl | MR

[14] K. Diederich and T. Ohsawa, Harmonic mappings and disc bundles over compact Kähler manifolds, Publ. R.I.M.S., 21 (1985), 819-833. | Zbl | MR

[15] P. Dolbeault, Formes différentielles et cohomologie sur une variété analytique complexe, I, Ann. of Math., 64 (1956), 83-130. | Zbl | MR

[16] 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. | Zbl | MR

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

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

[19] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160. | Zbl | MR

[20] H. Garland and M. S. Raghunathan, Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups, Ann. of Math., 92 (1970), 279-326. | Zbl | MR

[21] 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. | Zbl | MR | mathdoc-id

[22] M. Green and R. Lazarsfeld, Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese, and Beauville, Invent. Math., 90 (1987), 389-407. | Zbl | MR

[23] M. Green and R. Lazarsfeld, Higher obstructions to deforming cohomology groups of line bundles, Preprint (1990). | Zbl

[24] P. Griffiths, Periods of integrals on algebraic manifolds I, II, Amer. J. Math., 90 (1968), III, Publ. Math. I.H.E.S., 38 (1970). | Zbl

[25] P. Griffiths and J. Harris, Principles of Algebraic Geometric, John Wiley & Sons (1978). | Zbl

[26] P. Griffiths and W. Schmid, Locally homogeneous complex manifolds, Acta Math., 123 (1969), 253-302. | Zbl | MR

[27] R. Hain, The de Rham homotopy theory of complex algebraic varieties, I, K-Theory, 1 (1987), 271-324. | Zbl | MR

[28] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, New York, Academic Press (1978). | Zbl | MR

[29] P. W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett., 13, no. 16 (1964), 508-509. | MR

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

[31] G. Hochschild and G. D. Mostow, On the algebra of representative functions of an analytic group, Amer. J. Math., 83 (1961), 111-136. | Zbl | MR

[32] G. Hochschild, Coverings of pro-affine algebraic groups, Pacific J. Math., 35 (1970), 399-415. | Zbl | MR

[33] P. B. Kronheimer, M. J. Larsen and J. Scherk, Casson's invariant and quadratic reciprocity, Topology, 30 (1991), 335-338. | Zbl | MR

[34] M. Lubke, Chernklassen von Hermite-Einstein-vektorbundeln, Math. Ann., 260 (1982), 133-141. | Zbl | MR

[35] G. A. Margulis, Discrete groups of motions of manifolds of nonpositive curvature, Proc. Inter. Cong. Math. Vancouver (1974), v. 2, 21-34 ; transl. Amer. Math. Soc. Transl., 109 (1977), 33-45. | Zbl

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

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

[38] J. Morgan, The algebraic topology of smooth algebraic varieties, Publ. Math. I.H.E.S., 48 (1978), 137-204 ; and 64 (1985), 185. | Zbl | mathdoc-id

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

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

[41] M. V. Nori, On the representations of the fundamental group, Compositio Math., 33 (1976), 29-41. | Zbl | MR | mathdoc-id

[42] M. S. Ragunathan, Cohomology of arithmetic subgroups of algebraic groups, I, Ann. of Math., 86 (1967), 409-424 ; II, Ann. of Math., 87 (1968), 279-304. | Zbl

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

[44] J. H. Sampson, Applications of harmonic maps to Kähler geometry, Contemp. Math., 49 (1986), 125-133. | Zbl | MR

[45] J.-P. Serre, Linear Representations of Finite Groups, New York, Springer-Verlag (1977). | Zbl | MR

[46] C. T. Simpson, Systems of Hodge bundles and uniformization, doctoral dissertation, Harvard University (1987).

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

[48] C. T. Simpson, Transcendental aspects of the Riemann-Hilbert correspondence, Illinois J. of Math., 34 (1990), 368-391. | Zbl | MR

[49] Y. T. Siu, Complex analyticity of harmonic maps and strong rigidity of complex Kähler manifolds, Ann. of Math., 112 (1980), 73-110. | Zbl | MR

[50] T. Tannaka, Über den Dualitätssatz der nichtkommutativen topologischen Gruppen, Tohoku Math. J., 45 (1938), 1-12. | Zbl | JFM

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

[52] 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. | Zbl | MR

[53] A. Weil, Introduction à l'étude des variétés kähleriennes, Paris, Hermann (1952).

[54] A. Weil, Discrete subgroups of Lie group I, Ann. of Math., 72 (1960), 369-384 ; II, Ann. of Math., 75 (1962), 578-602 ; Remarks on the cohomology of groups, Ann. of Math., 80 (1964), 149-157. | Zbl | MR

[55] A. Weil, Basic Number Theory, New York, Springer-Verlag (1967). | Zbl | MR