Skip to main content
Log in

Hom stacks

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

An Erratum to this article was published on 01 August 2006

Abstract

We study Hom 2-functors parameterizing 1-morphisms of algebraic stacks, and prove that they are representable by algebraic stacks under certain conditions, using Artin's criterion. As an application we study Picard 2-functors which parameterize line bundles on algebraic stacks.

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. Compositio Mathematica 141, 19–34 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Artin, M.: Algebraization of formal moduli I. Global analysis, Univ. Tokyo Press, 1969, pp. 21–71

  3. Artin, M.: Versal deformation and algebraic stacks. Inventiones 27, 165–189 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  4. Deligne, P.: Theorie de Hodge III. Inst. Hautes Études Sci. Publ. Math. 44, 237–250 (1974)

    Article  Google Scholar 

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

  6. Faltings, G.: Finiteness of coherent cohomology for proper fppf stacks. J. Alg. Geom. 12, 357–366 (2003)

    MATH  MathSciNet  Google Scholar 

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

  8. Iwanari, I.: Formal algebraic stacks. In preparation

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

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

  11. Mumford, D.: Abelian Varieties. Tata Institute of Fundamental Research Studies in Mathematics 5, Oxford University Press, 1970

  12. Olsson, M.: Hom-stacks and restriction of scalars. To appear in Duke Math J.

  13. Olsson, M.: Deformation theory of representable morphisms of algebraic stacks. To appear in Math. Zeit

  14. Olsson, M.: On proper coverings of Artin stacks. To appear in Advances in Mathematics

  15. Olsson, M.: Sheaves on Artin stacks. To appear in J. Reine Angew. Math.

  16. Olsson, M., Starr, J.: Quot functors for Deligne-Mumford stacks. Commum. Alg. 31, 4069–4096 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Schlessinger, M.: Functors of Artin Rings. Trans. AMS 130, 208–222 (1968)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Masao Aoki.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s00229-006-0029-3.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aoki, M. Hom stacks. manuscripta math. 119, 37–56 (2006). https://doi.org/10.1007/s00229-005-0602-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-005-0602-1

Mathematics Subject Classification (2000)

Navigation