Projective modules over Laurent polynomial rings
Author:
Richard G. Swan
Journal:
Trans. Amer. Math. Soc. 237 (1978), 111-120
MSC:
Primary 13C10; Secondary 13F20, 14F05
DOI:
https://doi.org/10.1090/S0002-9947-1978-0469906-4
MathSciNet review:
0469906
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Quillen's solution of Serre's problem is extended to Laurent polynomial rings. An example is given of a -module P which is not extended even though A is regular and
is extended for all maximal ideals
of A.
- [1] H. Bass, Algebraic K-theory, Benjamin, New York, 1968. MR 40 #2736. MR 0249491 (40:2736)
- [2] -, Some problems in ``classical'' algebraic K-theory, Algebraic K-Theory, II (Proc. Conf., Seattle Res. Center, Battelle Mem. Inst., 1972), Lecture Notes in Math., vol. 342, Springer-Verlag, Berlin and New York, 1973, pp. 3-73. MR 48 #3656b. MR 0409606 (53:13358)
- [3] -, Libération des modules projectifs sur certains anneaux de polynômes, Séminaire Bourbaki 1973/1974, Exposé no. 448, Lecture Notes in Math., vol. 431, Springer-Verlag, Berlin and New York, 1975. pp. 228-254. MR 51 # 18. MR 0472826 (57:12516)
- [4] A. Borel and J.-P. Serre, Groupes de Lie et puissances réduites de Steenrod, Amer. J. Math. 75 (1953), 409-448. MR 15, 338. MR 0058213 (15:338b)
- [5]
J.-L. Loday, Applications algébriques du tore dans la sphère et de
dans
, Algebraic K-Theory, II (Proc. Conf., Seattle Res. Center, Battelle Memorial Inst., 1972), Lecture Notes in Math., vol. 342, Springer-Verlag, Berlin and New York, 1973, pp. 79-91. MR 51 #4276. MR 0368034 (51:4276)
- [6]
M. P. Murthy, Projective
-modules, J. London Math. Soc. 41 (1966), 453-456. MR 34 #188. MR 0200289 (34:188)
- [7] D. Quillen, Projective modules over polynomial rings. Invent. Math. 36 (1976), 167-171. MR 0427303 (55:337)
- [8] N. Steenrod, The topology of fibre bundles, Princeton Univ. Press, Princeton, N. J., 1951. MR 12,522. MR 0039258 (12:522b)
- [9] R. G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (1962), 264-277. MR 26 #785. MR 0143225 (26:785)
- [10] -, Serre's problem, Conf. on Commutative Algebra-1975 (A. Geramita, Editor), Queen's Papers in Pure and Appl. Math., no. 42, Queen's Univ., Kingston, Ontario, Canada. MR 0384769 (52:5642)
- [11] R. G. Swan and J. Towber, A class of projective modules which are nearly free, J. Algebra 36 (1975), 427-434. MR 0376682 (51:12857)
Retrieve articles in Transactions of the American Mathematical Society with MSC: 13C10, 13F20, 14F05
Retrieve articles in all journals with MSC: 13C10, 13F20, 14F05
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1978-0469906-4
Keywords:
Projective modules,
Laurent polynomial rings,
Serre's problem
Article copyright:
© Copyright 1978
American Mathematical Society