Higgs bundles and local systems

Carlos T. Simpson

Publications Mathématiques de l'IHÉS (1992)

  • Volume: 75, page 5-95
  • ISSN: 0073-8301

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Simpson, Carlos T.. "Higgs bundles and local systems." Publications Mathématiques de l'IHÉS 75 (1992): 5-95. <http://eudml.org/doc/104080>.

@article{Simpson1992,
author = {Simpson, Carlos T.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {variation; deformation; compact Kähler manifold; Higgs bundles; local systems; cohomology; Hodge structure},
language = {eng},
pages = {5-95},
publisher = {Institut des Hautes Études Scientifiques},
title = {Higgs bundles and local systems},
url = {http://eudml.org/doc/104080},
volume = {75},
year = {1992},
}

TY - JOUR
AU - Simpson, Carlos T.
TI - Higgs bundles and local systems
JO - Publications Mathématiques de l'IHÉS
PY - 1992
PB - Institut des Hautes Études Scientifiques
VL - 75
SP - 5
EP - 95
LA - eng
KW - variation; deformation; compact Kähler manifold; Higgs bundles; local systems; cohomology; Hodge structure
UR - http://eudml.org/doc/104080
ER -

References

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  1. [1] L. V. AHLFORS, An extension of Schwarz's lemma, Trans. Amer. Math. Soc., 43, no. 3 (1938), 359-364. Zbl0018.41002MR1501949JFM64.0315.04
  2. [2] H. BASS, Groups of integral representation type, Pacific J. of Math., 86 (1980), 15-51. Zbl0444.20006MR82c:20014
  3. [3] A. BOREL and W. CASSELMAN, L2-cohomology of locally symmetric manifolds of finite volume, Duke Math. J., 50 (1983), 625-647. Zbl0528.22012MR86j:22015
  4. [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. Zbl0695.58010MR91c:58032
  5. [5] K. CORLETTE, Flat G-bundles with canonical metrics, J. Diff. Geom., 28 (1988), 361-382. Zbl0676.58007MR89k:58066
  6. [6] K. CORLETTE, Rigid representations of Kählerian fundamental groups, J. Diff. Geom., 33 (1991), 239-252. Zbl0731.53061MR91k:32018
  7. [7] P. DELIGNE, letter to J.-P. Serre (1968). 
  8. [8] P. DELIGNE, Un théorème de finitude pour la monodromie, Discrete Groups in Geometry and Analysis, Birkhauser (1987), 1-19. Zbl0656.14010MR88h:14013
  9. [9] P. DELIGNE, La conjecture de Weil pour les surfaces K3, Invent. Math., 15 (1972), 206-222. Zbl0219.14022MR45 #5137
  10. [10] P. DELIGNE, Theorie de Hodge, II, Publ. Math. I.H.E.S., 40 (1971), 5-58. Zbl0219.14007MR58 #16653a
  11. [11] P. DELIGNE, Travaux de Shimura, Séminaire Bourbaki, Lect. Notes in Math., 244 (1971), 123-165. Zbl0225.14007MR58 #16675
  12. [12] P. DELIGNE, P. GRIFFITHS, J. MORGAN and D. SULLIVAN, Real homotopy theory of Kähler manifolds, Invent. Math., 29 (1975), 245-274. Zbl0312.55011MR52 #3584
  13. [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. Zbl0465.00010MR84m:14046
  14. [14] K. DIEDERICH and T. OHSAWA, Harmonic mappings and disc bundles over compact Kähler manifolds, Publ. R.I.M.S., 21 (1985), 819-833. Zbl0601.32023MR87g:32017
  15. [15] P. DOLBEAULT, Formes différentielles et cohomologie sur une variété analytique complexe, I, Ann. of Math., 64 (1956), 83-130. Zbl0072.40603MR18,670e
  16. [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. Zbl0529.53018MR86h:58038
  17. [17] S. K. DONALDSON, Infinite determinants, stable bundles, and curvature, Duke Math. J., 54 (1987), 231-247. Zbl0627.53052MR88g:32046
  18. [18] S. K. DONALDSON, Twisted harmonic maps and self-duality equations, Proc. London Math. Soc., 55 (1987), 127-131. Zbl0634.53046MR88g:58040
  19. [19] J. EELLS and J. H. SAMPSON, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160. Zbl0122.40102MR29 #1603
  20. [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. Zbl0206.03603MR42 #1943
  21. [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. Zbl0678.53059MR90b:32041
  22. [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. Zbl0659.14007MR89b:32025
  23. [23] M. GREEN and R. LAZARSFELD, Higher obstructions to deforming cohomology groups of line bundles, Preprint (1990). Zbl0735.14004
  24. [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). Zbl0188.24801
  25. [25] P. GRIFFITHS and J. HARRIS, Principles of Algebraic Geometric, John Wiley & Sons (1978). Zbl0408.14001
  26. [26] P. GRIFFITHS and W. SCHMID, Locally homogeneous complex manifolds, Acta Math., 123 (1969), 253-302. Zbl0209.25701MR41 #4587
  27. [27] R. HAIN, The de Rham homotopy theory of complex algebraic varieties, I, K-Theory, 1 (1987), 271-324. Zbl0637.55006MR88h:14029
  28. [28] S. HELGASON, Differential geometry, Lie groups, and symmetric spaces, New York, Academic Press (1978). Zbl0451.53038MR80k:53081
  29. [29] P. W. HIGGS, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett., 13, no. 16 (1964), 508-509. MR30 #5738
  30. [30] N. J. HITCHIN, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3), 55 (1987), 59-126. Zbl0634.53045MR89a:32021
  31. [31] G. HOCHSCHILD and G. D. MOSTOW, On the algebra of representative functions of an analytic group, Amer. J. Math., 83 (1961), 111-136. Zbl0116.02203MR25 #5129
  32. [32] G. HOCHSCHILD, Coverings of pro-affine algebraic groups, Pacific J. Math., 35 (1970), 399-415. Zbl0205.25103MR43 #4830
  33. [33] P. B. KRONHEIMER, M. J. LARSEN and J. SCHERK, Casson's invariant and quadratic reciprocity, Topology, 30 (1991), 335-338. Zbl0729.57007MR92g:57028
  34. [34] M. LUBKE, Chernklassen von Hermite-Einstein-vektorbundeln, Math. Ann., 260 (1982), 133-141. Zbl0471.53043MR83m:32031
  35. [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. Zbl0367.57012
  36. [36] V. B. MEHTA and A. RAMANATHAN, Semistable sheaves on projective varieties and their restriction to curves, Math. Ann., 258 (1982), 213-224. Zbl0473.14001MR83f:14013
  37. [37] V. B. MEHTA and A. RAMANATHAN, Restriction of stable sheaves and representations of the fundamental group, Invent. Math., 77 (1984), 163-172. Zbl0525.55012MR85m:14026
  38. [38] J. MORGAN, The algebraic topology of smooth algebraic varieties, Publ. Math. I.H.E.S., 48 (1978), 137-204 ; and 64 (1985), 185. Zbl0401.14003
  39. [39] M. S. NARASIMHAN and C. S. SESHADRI, Stable and unitary bundles on a compact Riemann surface, Ann. of Math., 82 (1965), 540-564. Zbl0171.04803MR32 #1725
  40. [40] N. NITSURE, Moduli spaces of semistable pairs on a curve, Proc. London Math. Soc. 62 (1991), 275-300. Zbl0733.14005MR92a:14010
  41. [41] M. V. NORI, On the representations of the fundamental group, Compositio Math., 33 (1976), 29-41. Zbl0337.14016MR54 #5237
  42. [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. Zbl0157.06802
  43. [43] N. SAAVEDRA RIVANO, Catégories tannakiennes, Lect. Notes in Math., 265, Heidelberg, Springer-Verlag (1972). Zbl0241.14008MR49 #2769
  44. [44] J. H. SAMPSON, Applications of harmonic maps to Kähler geometry, Contemp. Math., 49 (1986), 125-133. Zbl0605.58019MR87g:58028
  45. [45] J.-P. SERRE, Linear Representations of Finite Groups, New York, Springer-Verlag (1977). Zbl0355.20006MR56 #8675
  46. [46] C. T. SIMPSON, Systems of Hodge bundles and uniformization, doctoral dissertation, Harvard University (1987). 
  47. [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. Zbl0669.58008MR90e:58026
  48. [48] C. T. SIMPSON, Transcendental aspects of the Riemann-Hilbert correspondence, Illinois J. of Math., 34 (1990), 368-391. Zbl0727.34007MR91b:14009
  49. [49] Y. T. SIU, Complex analyticity of harmonic maps and strong rigidity of complex Kähler manifolds, Ann. of Math., 112 (1980), 73-110. Zbl0517.53058MR81j:53061
  50. [50] T. TANNAKA, Über den Dualitätssatz der nichtkommutativen topologischen Gruppen, Tohoku Math. J., 45 (1938), 1-12. Zbl0020.00904JFM64.0362.01
  51. [51] K. K. UHLENBECK, Connections with Lp bounds on curvature, Comm. Math. Phys., 83 (1982), 31-42. Zbl0499.58019MR83e:53035
  52. [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. Zbl0615.58045MR88i:58154
  53. [53] A. WEIL, Introduction à l'étude des variétés kähleriennes, Paris, Hermann (1952). 
  54. [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. Zbl0131.26602MR25 #1241
  55. [55] A. WEIL, Basic Number Theory, New York, Springer-Verlag (1967). Zbl0176.33601MR38 #3244

Citations in EuDML Documents

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  1. Indranil Biswas, Carlos Florentino, Higgs bundles and representation spaces associated to morphisms
  2. Indranil Biswas, Carlos Florentino, [unknown]
  3. Toshitake Kohno, Andrei Pajitnov, Novikov homology, jump loci and Massey products
  4. M. Rapoport, M. Richartz, On the classification and specialization of F -isocrystals with additional structure
  5. Daniele Angella, Hisashi Kasuya, Hodge theory for twisted differentials
  6. Indranil Biswas, Oscar García-Prada, Jacques Hurtubise, Pseudo-real principal Higgs bundles on compact Kähler manifolds
  7. Martin Schottenloher, Metaplectic Quantization of the Moduli Spaces of Flat and Parabolic Bundles
  8. Adrian Langer, On the S-fundamental group scheme
  9. Claude Sabbah, Non-commutative Hodge structures
  10. Katsutoshi Yamanoi, On fundamental groups of algebraic varieties and value distribution theory

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