Skip to main content
Log in

Deformation theory of representable morphisms of algebraic stacks

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

Abstract

We study the relationship between the deformation theory of representable 1-morphisms between algebraic stacks and the cotangent complex defined by Laumon and Moret-Bailly.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aoki, M.: Deformation theory of algebraic stacks. Comp. Math. 141, 19–34 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Artin, M.: Versal deformations and algebraic stacks. Invent. Math. 27, 165–189 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  3. Artin, M., Grothendieck, A., Verdier, J.-L.: Théorie des topos et cohomologie étale des schémas. Lecture Notes in Mathematics 269, 270, 305, Springer-Verlag, Berlin 1971

  4. Behrend, K., Fantechi, B.: The intrinsic normal cone. Inv. Math. 128, 45–88 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Deligne, P.: Théorie de Hodge. III. Inst. Hautes Études Sci. Publ. Math. 44, 5–78 (1974)

    MATH  MathSciNet  Google Scholar 

  6. Demazure, M., Grothendieck, A.: Schémas en groupes. Lecture Notes in Mathematics 151, 152, 153, Springer-Verlag, Berlin 1970

  7. Dieudonné, J., Grothendieck, A.: Éléments de géométrie algébrique. Inst. Hautes Études Sci. Publ. Math. 4, 8, 11, 17, 20, 24, 28, 32 (1961–1967).

  8. Grothendieck, A.: Revêtements Étales et Groupe Fondamental. Lecture Notes in Mathematics 224, Springer–Verlag, Berlin 1971

  9. Grothendieck, A.: Catégories cofibrées additives et Complexe cotangent relatif. Lecture Notes in Mathematics 79, Springer–Verlag, Berlin 1968

  10. Illusie, L.: Complexe cotangent et déformations. I. Lecture Notes in Mathematics 239, Springer-Verlag, Berlin 1971

  11. Illusie, L.: Complexe cotangent et déformations. II. Lecture Notes in Mathematics 283, Springer-Verlag, Berlin 1972

  12. Knutson, D.: Algebraic spaces. Lecture Notes in Mathematics 203, Springer-Verlag, Berlin 1971

  13. Laumon, G., Moret-Bailly, L.: Champs algébriques. Ergebnisse der Mathematik 39, Springer-Verlag, Berlin 2000

  14. Olsson, M.: The logarithmic cotangent complex. preprint 2002

  15. Olsson, M.: Sheaves on Artin stacks. preprint 2005

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martin C. Olsson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Olsson, M. Deformation theory of representable morphisms of algebraic stacks. Math. Z. 253, 25–62 (2006). https://doi.org/10.1007/s00209-005-0875-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-005-0875-9

Keywords

Navigation