Skip to main content
SpringerLink
Log in

Langlands duality for Hitchin systems

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Argyres, P., Kapustin, A., Seiberg, N.: On S-duality for non-simply-laced gauge groups. J. High Energy Phys. (6), 043 (2006)

  2. Arinkin, D.: Fourier transform for quantized completely integrable systems. PhD thesis, Harvard University (2002)

  3. Artin, M., Grothendieck, A., Verdier, J.-L.: Théorie des topos et cohomologie étale des schémas. Lecture Notes in Math., vols. 269, 270, 305. Springer, Berlin (1972/1973)

    Google Scholar 

  4. Ben-Bassat, O.: Twisting derived equivalences. Trans. Am. Math. Soc. 361(10), 5469–5504 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bezrukavnikov, R., Braverman, A.: Geometric Langlands correspondence for D-modules in prime characteristic: the GL(n) case. Pure Appl. Math. Q. 3(1), 153–179 (2007), part 3

    MathSciNet  MATH  Google Scholar 

  6. Beilinson, A., Bernstein, J., Deligne, P: Faisceaux pervers. In: Analysis and Topology on Singular Spaces, I, Luminy, 1981. Astérisque, vol. 100, pp. 5–171. Soc. Math. France, Paris (1982)

    Google Scholar 

  7. Beilinson, A., Drinfeld, V.: Quantization of Hitchin’s Integrable System and Hecke Eigensheaves. Book (2003, in preparation)

  8. Bershadsky, M., Johansen, A., Sadov, V., Vafa, C.: Topological reduction of 4D SYM to 2D σ-models. Nucl. Phys. B 448(1–2), 166–186 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  9. Breen, L.: The cube structure on the determinant bundle. In: Theta Functions—Bowdoin 1987, Brunswick, ME, 1987. Proc. Sympos. Pure Math., vol. 49, pp. 663–673. Am. Math. Soc., Providence (1989), part 1

    Google Scholar 

  10. Breen, L.: Bitorseurs et cohomologie non abélienne. In: The Grothendieck Festschrift, vol. I. Progr. Math., vol. 86, pp. 401–476. Birkhäuser, Boston (1990)

    Google Scholar 

  11. Diaconescu, D.-E., Donagi, R., Dijkgraaf, R., Hofman, C., Pantev, T.: Geometric transitions and integrable systems. Nucl. Phys. B 752(3), 329–390 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Diaconescu, D.E., Donagi, R., Pantev, T.: Intermediate Jacobians and ADE Hitchin systems. Math. Res. Lett. 14(5), 745–756 (2007)

    MathSciNet  MATH  Google Scholar 

  13. Donagi, R., Gaitsgory, D.: The gerbe of Higgs bundles. Transform. Groups 7(2), 109–153 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dimca, A.: Sheaves in Topology. Universitext. Springer, Berlin, (2004)

    Book  Google Scholar 

  15. Donagi, R.: Decomposition of spectral covers. Astérisque 218, 145–175 (1993)

    MathSciNet  Google Scholar 

  16. Donagi, R.: Spectral covers. In: Current Topics in Complex Algebraic Geometry, Berkeley, CA, 1992/1993. Math. Sci. Res. Inst. Publ., vol. 28, pp. 65–86. Cambridge Univ. Press, Cambridge (1995)

    Google Scholar 

  17. Donagi, R., Pantev, T.: Torus fibrations, gerbes, and duality, with an appendix by D. Arinkin. Mem. Am. Math. Soc. 193, 90 (2008)

    MathSciNet  Google Scholar 

  18. Drinfeld, V.: Two-dimensional l-adic representations of the fundamental group of a curve over a finite field and automorphic forms on GL (2). Am. J. Math. 105(1), 85–114 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  19. Faltings, G.: Stable G-bundles and projective connections. J. Algebr. Geom. 2(3), 507–568 (1993)

    MathSciNet  MATH  Google Scholar 

  20. Frenkel, E., Gaitsgory, D., Vilonen, K.: On the geometric Langlands conjecture. J. Am. Math. Soc. 15(2), 367–417 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gaitsgory, D.: Geometric Langlands correspondence for GL  n . In: Proceedings of the International Congress of Mathematicians, vol. II, Beijing, 2002, pp. 571–582 (2002)

    Google Scholar 

  22. Gelfand, S., Manin, Y.: Methods of Homological Algebra. Springer Monographs in Mathematics, 2nd edn. Springer, Berlin (2003)

    MATH  Google Scholar 

  23. Grothendieck, A.: Sur quelques points d’algébre homologique. Tohoku Math. J. 119 (1957)

  24. Hitchin, N.: Stable bundles and integrable systems. Duke Math. J. 54(1), 91–114 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  25. Hitchin, N.: Lie groups and Teichmüller space. Topology 31(3), 449–473 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  26. Hausel, T., Thaddeus, M.: Mirror symmetry, Langlands duality, and the Hitchin system. Invent. Math. 153(1), 197–229 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  27. Iversen, B.: Cohomology of Sheaves. Universitext. Springer, Berlin (1986)

    Book  Google Scholar 

  28. Kostant, B.: Lie group representations on polynomial rings. Am. J. Math. 85, 327–404 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  29. Kapustin, A., Witten, E.: Electric-magnetic duality and the geometric Langlands program. Commun. Number Theory Phys. 1(1), 1–236 (2007)

    MathSciNet  MATH  Google Scholar 

  30. Laumon, G.: Transformation de Fourier généralisée. Preprint. aXiv:alg-geom/9603004

  31. Looijenga, E.: Cohomology and intersection homology of algebraic varieties. In: Complex Algebraic Geometry, Park City, UT, 1993. IAS/Park City Math. Ser., vol. 3, pp. 221–263. Am. Math. Soc., Providence (1997)

    Google Scholar 

  32. Mumford, D.: Abelian Varieties. With Appendices by C.P. Ramanujam and Yuri Manin. Corrected Reprint of the Second (1974) edn. Tata Institute Fundamental Research Studies in Mathematics, vol. 5. Hindustan Book Agency, New Delhi (2008), xii+263 pp. Published for the Tata Institute of Fundamental Research, Bombay

    Google Scholar 

  33. Saito, M.: Mixed Hodge modules. Publ. Res. Inst. Math. Sci. 26(2), 221–333 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  34. Scognamillo, R.: An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups. Compos. Math. 110(1), 17–37 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  35. Simpson, C.: Moduli of representations of the fundamental group of a smooth projective variety—I. Publ. Math. Inst. Ht. Études Sci. 79, 47–129 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  36. Simpson, C.: Moduli of representations of the fundamental group of a smooth projective variety—II. Publ. Math. Inst. Ht. Études Sci. 80, 5–79 (1995)

    Article  MATH  Google Scholar 

  37. Simpson, C.: The Hodge filtration on nonabelian cohomology. In: Algebraic Geometry, Santa Cruz, 1995. Proc. Sympos. Pure Math., vol. 62, pp. 217–281 (1997), part 2

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA

    R. Donagi & T. Pantev

Authors
  1. R. Donagi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Pantev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Pantev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Donagi, R., Pantev, T. Langlands duality for Hitchin systems. Invent. math. 189, 653–735 (2012). https://doi.org/10.1007/s00222-012-0373-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-012-0373-8

Keywords

Search

Navigation