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Quillen's solution of Serre's Problem

  • Andrei Suslin (a1)

In this note we recall the history of Serre's problem and its beautiful solution given by D. Quillen in 1976

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1.Bass, H., K-Theory and Stable Algebra, Publ. Math. IHES 22 (1964), 560.
2.Bass, H., Connell, E.H., and Wright, D.L., Locally Polynomial Algebras are Symmetric Algebras, Invent. Math. 38 (1977), 279299.
3.Horrocs, G., Projective modules over an extension of a Local Ring, Proc. London Math. Soc. 14 (1964), 714718.
4.Murthy, M.P. and Towber, J., Algebraic Vector Bundles over A3 are trivial, Invent. Math. 24 (1974), 173189.
5.Quillen, D., Projective Modules over Polynomial Rings, Invent. Math. 36 (1976), 166172.
6.Serre, J.-P., Faisceaux Algebriques Coherents, Annals of Math. 61 (1955), 197278.
7.Serre, J.-P., Modules Projectifs et espace fibres a fibre vectoriel, Seminaire P. Dubreil 11 (1958), 118.
8.Seshadri, C.S., Triviality of Vector Bundles over the Affine Space K2, Proc. Nat. Acad. Sci. USA 44 (1958), 456458.
9.Suslin, A., On Projective Modules over Polynomial Rings, Math USSR Sbornik, 22 (1974), 595602.
10.Suslin, A., Projective Modules over Polynomial Rings are Free, Soviet Math. Dokl. 17 (1976), 11601164.
11.Suslin, A., On the Structure of the Special Linear Group over Polynomial Rings, Math USSR Izv. 11 (1977), 221238.
12.Tulenbaev, M.S.Steinberg Group over Polynomial Rings, Math USSR Sbornik 45 (1983), 139154.
13.Vasserstein, L. and Suslin, A., Serre's Problem on Projective Modules over Polynomial Rings and Algebraic K-Theory, Math. USSR Izv. 10 (1976), 9371001.
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Journal of K-Theory
  • ISSN: 1865-2433
  • EISSN: 1865-5394
  • URL: /core/journals/journal-of-k-theory
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