Tannakian Categories

  • P. Deligne
  • J. S. Milne
Part of the Lecture Notes in Mathematics book series (LNM, volume 900)

Abstract

In the first section it is shown how to introduce on an abstract category operations of tensor products and duals having properties similar to the familiar operations on the category Vec k of finite-dimensional vector spaces over a field k. What complicates this is the necessity of including enough constraints so that, whenever an obvious isomorphism (e.g., Open image in new window exists in Vec k, a unique isomorphism is constrained to exist also in the abstract setting.

References

  1. 1.
    Abhyankar, S. Resolution of Singularities of Embedded Algebraic Surfaces, Academic Press, 1966.Google Scholar
  2. 1.
    Bourbaki, N. Algèbre; Modules et Anneaux Semi-Simples. Hermann, Paris (1958).Google Scholar
  3. 2.
    Bourbaki, N. Algèbre Commutative; Modules Plats, Localisation. Hermann, Paris (1961).Google Scholar
  4. 1.
    Deligne, P. La conjecture de Weil pour les surfaces K3, Invent. Math. 15 (1972) 206–222.MATHCrossRefMathSciNetGoogle Scholar
  5. 2.
    Deligne, P. Valeurs de fonctions L et périodes d’integrales. Proc. Symp. Pure Math., A.M.S., 33 (1979) part 2, 313–346.MathSciNetGoogle Scholar
  6. 1.
    Giraud, J. Cohomologie Non Abélienne, Springer, Heidelberg, 1971.MATHGoogle Scholar
  7. 1.
    Hochschild, G. The Structure of Lie Groups, Holden-Day, San Francisco, 1965.MATHGoogle Scholar
  8. 1.
    Humphries, J. Introduction to Lie Algebras and Representation Theory, Springer, Heidelberg, 1972.Google Scholar
  9. 1.
    Kuga, M. and Satake, I. Abelian varieties attached to polarized K3-surfaces, Math. Ann. 169 (1967) 239–242.MATHCrossRefMathSciNetGoogle Scholar
  10. 1.
    MacLane, S. Natural associativity and commutativity. Rice University Studies 69 (1963) 28–46.MathSciNetGoogle Scholar
  11. 2.
    MacLane, S. Categories for the Working Mathematician. Springer, Heidelberg, 1972.Google Scholar
  12. 1.
    Mumford, D. Abelian Varieties, Oxford U.P., Oxford, 1970.MATHGoogle Scholar
  13. 1.
    Nori, M. On the representations of the fundamental group. Compositio Math. 33 (1976) 29–41.MATHMathSciNetGoogle Scholar
  14. 1.
    Saavedra Rivano, N. Catégories Tannakiennes, Lecture Notes in Math 265, Springer, Heidelberg, 1972.MATHGoogle Scholar
  15. 1.
    Serre, J.-P. Cohomologie Galoisienne, Lecture Notes in Math 5, Springer, Heidelberg, 1964.MATHGoogle Scholar
  16. 2.
    Serre, J.-P. Groupes algébriques associés aux modules de Hodge-Tate, (Journées de Géométrie Algébrique de Rennes), Astérisque 65 (1979) 155–187.MATHMathSciNetGoogle Scholar
  17. 1.
    Springer, T. Reductive groups, Proc. Symp. Pure Math., A.M.S., 33 (1979) part 1, 3–27.MathSciNetGoogle Scholar
  18. 1.
    Waterhouse, W. Introduction to Affine Group Schemes, Springer, Heidelberg, 1979.MATHGoogle Scholar
  19. 1.
    Wells, R. Differential Analysis on Complex Manifolds. Prentice-Hall, Englewood Cliffs, 1973.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • P. Deligne
  • J. S. Milne

There are no affiliations available

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