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Quillen's solution of Serre's Problem

Published online by Cambridge University Press:  11 March 2013

Andrei Suslin*
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, ILL, [email protected]
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Abstract

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

Type
Research Article
Copyright
Copyright © ISOPP 2013 

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References

REFERENCES

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