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On Moduli Stacks of G-bundles over a Curve

  • Norbert Hoffmann
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Let C be a smooth projective curve over an algebraically closed field k of arbitrary characteristic. Given a linear algebraic group G over k, let M G be the moduli stack of principal G-bundles on C. We determine the set of connected components π0(MG) for smooth connected groups G.

Mathematics Subject Classification (2000)

14D20 14F05 

Keywords

Principal bundle algebraic curve moduli stack 

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References

  1. [1]
    K. Behrend. The Lefschetz Trace Formula for the Moduli Stack of Principal Bundles. PhD thesis, Berkeley, 1991. http://www.math.ubc.ca/∼behrend/thesis.html.Google Scholar
  2. [2]
    I. Biswas and N. Hoffmann. The Line Bundles on Moduli Stacks of Principal Bundles on a Curve. Documenta Math. 15:35–72, 2010.zbMATHMathSciNetGoogle Scholar
  3. [3]
    A. Borel. Linear algebraic groups. New York — Amsterdam: W.A. Benjamin, 1969.zbMATHGoogle Scholar
  4. [4]
    C. Chevalley. Les isogénies. Séminaire C. Chevalley 1956–1958: Classification des groupes de Lie algébriques, Exposé 18. Paris: Secrétariat mathématique, 1958.Google Scholar
  5. [5]
    M. Demazure and P. Gabriel. Groupes algébriques. Tome I. Amsterdam: North-Holland Publishing Company, 1970.zbMATHGoogle Scholar
  6. [6]
    V.G. Drinfeld and C. Simpson. B-structures on G-bundles and local triviality. Math. Res. Lett., 2(6):823–829, 1995.zbMATHMathSciNetGoogle Scholar
  7. [7]
    J. Giraud. Cohomologie non abelienne. Grundlehren, Band 179. Berlin-Heidelberg-New York: Springer-Verlag, 1971.zbMATHGoogle Scholar
  8. [8]
    A. Grothendieck. Le groupe de Brauer. III: Exemples et complements. Dix exposés sur la cohomologie des schémas, Advanced Studies Pure Math. 3, 88–188, 1968.MathSciNetGoogle Scholar
  9. [9]
    A. Grothendieck et al. SGA 1: Revêtements étales et groupe fondamental. Lecture Notes in Mathematics, Vol. 224. Springer-Verlag, Berlin, 1971.Google Scholar
  10. [10]
    A. Grothendieck et al. SGA 4: Théorie des topos et cohomologie étale des schémas. Tome 2. Lecture Notes in Mathematics, Vol. 270. Springer-Verlag, Berlin, 1972.Google Scholar
  11. [11]
    Y.I. Holla. Parabolic reductions of principal bundles. Preprint math.AG/0204219. Available at http://www.arXiv.org.Google Scholar
  12. [12]
    G. Laumon and L. Moret-Bailly. Champs algébriques. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, Band 39. Berlin: Springer, 2000.Google Scholar
  13. [13]
    F. Orgogozo. Altérations et groupe fondamental premier à p. Bull. Soc. Math. Fr., 131(1):123–147, 2003.zbMATHMathSciNetGoogle Scholar
  14. [14]
    M. Raynaud. Revêtements de la droite affine en caractéristique p > 0 et conjecture d’Abhyankar. Invent. Math., 116(1-3):425–462, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    C. Sorger. Lectures on moduli of principal G-bundles over algebraic curves. in: L. Göttsche (ed.), Moduli Spaces in Algebraic Geometry (Trieste, ICTP, 1999), 1–57. Available at http://users.ictp.it/∼pub_off/lectures/vol1.html.Google Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Norbert Hoffmann
    • 1
  1. 1.Mathematisches Institut der Freien UniversitätBerlinGermany

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