Advertisement

Mathematische Zeitschrift

, Volume 253, Issue 1, pp 25–62 | Cite as

Deformation theory of representable morphisms of algebraic stacks

  • Martin C. OlssonEmail author
Article

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.

Keywords

Deformation Theory Algebraic Stack Cotangent Complex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aoki, M.: Deformation theory of algebraic stacks. Comp. Math. 141, 19–34 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Artin, M.: Versal deformations and algebraic stacks. Invent. Math. 27, 165–189 (1974)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 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 1971Google Scholar
  4. 4.
    Behrend, K., Fantechi, B.: The intrinsic normal cone. Inv. Math. 128, 45–88 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Deligne, P.: Théorie de Hodge. III. Inst. Hautes Études Sci. Publ. Math. 44, 5–78 (1974)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Demazure, M., Grothendieck, A.: Schémas en groupes. Lecture Notes in Mathematics 151, 152, 153, Springer-Verlag, Berlin 1970Google Scholar
  7. 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).Google Scholar
  8. 8.
    Grothendieck, A.: Revêtements Étales et Groupe Fondamental. Lecture Notes in Mathematics 224, Springer–Verlag, Berlin 1971Google Scholar
  9. 9.
    Grothendieck, A.: Catégories cofibrées additives et Complexe cotangent relatif. Lecture Notes in Mathematics 79, Springer–Verlag, Berlin 1968Google Scholar
  10. 10.
    Illusie, L.: Complexe cotangent et déformations. I. Lecture Notes in Mathematics 239, Springer-Verlag, Berlin 1971Google Scholar
  11. 11.
    Illusie, L.: Complexe cotangent et déformations. II. Lecture Notes in Mathematics 283, Springer-Verlag, Berlin 1972Google Scholar
  12. 12.
    Knutson, D.: Algebraic spaces. Lecture Notes in Mathematics 203, Springer-Verlag, Berlin 1971Google Scholar
  13. 13.
    Laumon, G., Moret-Bailly, L.: Champs algébriques. Ergebnisse der Mathematik 39, Springer-Verlag, Berlin 2000Google Scholar
  14. 14.
    Olsson, M.: The logarithmic cotangent complex. preprint 2002Google Scholar
  15. 15.
    Olsson, M.: Sheaves on Artin stacks. preprint 2005Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrinceton08540USA

Personalised recommendations