On Moduli Stacks of G-bundles over a Curve

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


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 


Principal bundle algebraic curve moduli stack 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. Behrend. The Lefschetz Trace Formula for the Moduli Stack of Principal Bundles. PhD thesis, Berkeley, 1991.∼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 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∼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

Personalised recommendations