Hodge Cycles, Motives, and Shimura Varieties pp 419-419 | Cite as
Tannakian Categories
Erratum
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.Abhyankar, S. Resolution of Singularities of Embedded Algebraic Surfaces, Academic Press, 1966.Google Scholar
- 1.Bourbaki, N. Algèbre; Modules et Anneaux Semi-Simples. Hermann, Paris (1958).Google Scholar
- 2.Bourbaki, N. Algèbre Commutative; Modules Plats, Localisation. Hermann, Paris (1961).Google Scholar
- 1.Deligne, P. La conjecture de Weil pour les surfaces K3, Invent. Math. 15 (1972) 206–222.MATHCrossRefMathSciNetGoogle Scholar
- 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
- 1.Giraud, J. Cohomologie Non Abélienne, Springer, Heidelberg, 1971.MATHGoogle Scholar
- 1.Hochschild, G. The Structure of Lie Groups, Holden-Day, San Francisco, 1965.MATHGoogle Scholar
- 1.Humphries, J. Introduction to Lie Algebras and Representation Theory, Springer, Heidelberg, 1972.Google Scholar
- 1.Kuga, M. and Satake, I. Abelian varieties attached to polarized K3-surfaces, Math. Ann. 169 (1967) 239–242.MATHCrossRefMathSciNetGoogle Scholar
- 1.MacLane, S. Natural associativity and commutativity. Rice University Studies 69 (1963) 28–46.MathSciNetGoogle Scholar
- 2.MacLane, S. Categories for the Working Mathematician. Springer, Heidelberg, 1972.Google Scholar
- 1.Mumford, D. Abelian Varieties, Oxford U.P., Oxford, 1970.MATHGoogle Scholar
- 1.Nori, M. On the representations of the fundamental group. Compositio Math. 33 (1976) 29–41.MATHMathSciNetGoogle Scholar
- 1.Saavedra Rivano, N. Catégories Tannakiennes, Lecture Notes in Math 265, Springer, Heidelberg, 1972.MATHGoogle Scholar
- 1.Serre, J.-P. Cohomologie Galoisienne, Lecture Notes in Math 5, Springer, Heidelberg, 1964.MATHGoogle Scholar
- 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
- 1.Springer, T. Reductive groups, Proc. Symp. Pure Math., A.M.S., 33 (1979) part 1, 3–27.MathSciNetGoogle Scholar
- 1.Waterhouse, W. Introduction to Affine Group Schemes, Springer, Heidelberg, 1979.MATHGoogle Scholar
- 1.Wells, R. Differential Analysis on Complex Manifolds. Prentice-Hall, Englewood Cliffs, 1973.MATHGoogle Scholar
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