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Book Information
Author(s):
T. Y. Lam
Title:
Serre's problem on projective modules
Additional book information:
Springer Monographs in Mathematics,
Springer, Berlin, Heidelberg, New York,
2006,
xxi + 401 pp.,
US$99.00,
ISBN 978-3-540-23317-6
References:
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- 1.
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- 2.
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- 3.
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- 4.
- H. Bass, Some problems in `classical' algebraic K-theory, Algebraic K-Theory II, Lecture Notes in Math. 342, 1-70, Springer-Verlag, New York, 1973. MR 0409606 (53:13358)
- 5.
- D. Eisenbud and G. Evans, Generating modules efficiently: Theorems from algebraic K-theory, J. Alg. 27 (1973), 278-305. MR 0327742 (48:6084)
- 6.
- H. Grauert, Analytische Faserungen über holomorph-vollständigen Räumen, Math. Ann. 135 (1958), 263-273. MR 0098199 (20:4661)
- 7.
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- 8.
- G. Horrocks, Projective modules over an extension of a local ring, Proc. London Math. Soc. 14 (1964), 714-718. MR 0169878 (30:121)
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- 10.
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- 11.
- M. P. Murthy, Projective
-modules, J. London Math. Soc. 41 (1966), 453-456. MR 0200289 (34:188) - 12.
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are trivial, Invent. Math. 24 (1974), 173-189. MR 0422276 (54:10267) - 13.
- Parimala, Failure of a quadratic analogue of Serre's conjecture, Amer. J. Math. 100 (1978), 913-924. MR 517136 (84d:13016)
- 14.
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- 15.
- D. Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167-171. MR 0427303 (55:337)
- 16.
- R. A. Rao, The Bass-Quillen conjecture in dimension 3 but characteristic
via a question of A. Suslin, Invent. Math. 93 (1988), 609-618. MR 952284 (89d:13011) - 17.
- M. Roitman, On Serre's problem on projective modules, Proc. Amer. Math. Soc. 50 (1975), 45-52. MR 0387266 (52:8109)
- 18.
- C. S. Seshadri, Triviality of vector bundles over the affine space
, Proc. Nat'l. Acad. Sci. USA 44 (1958), 456-458. MR 0102527 (21:1318) - 19.
- J-P. Serre, Faisceaux algébrique coherént, Ann. of Math. 61 (1955), 191-278. MR 0068874 (16:953c)
- 20.
- J-P. Serre, Modules projectifs et espaces fibrés à fibre vectorielle, Sem. Dubreil-Pisot no. 23, Paris, 1957/1958. MR 0177011 (31:1277)
- 21.
- J-P. Serre, Sur les modules projectifs, Sem. Dubreil-Pisot no. 2, Paris, 1960/1961.
- 22.
- N. E. Steenrod, The Topology of Fibre Bundles, Princeton, 1951.
- 23.
- A. A. Suslin, Projective modules over a polynomial ring are free, Dokl. Akad Nauk SSSR 229 (1976), 1063-1066 (Soviet Math. Doklady 17 (1976), 1160-1164). MR 0469905 (57:9685)
- 24.
- A. A. Suslin, Stably free modules, Math. Sbornik (N.S.) 102 (1977), 537-550 (Math. USSR Sbornik 31 (1977), 479-491). MR 0441949 (56:340)
- 25.
- A. A. Suslin, On the structure of the special linear group over polynomial rings, Izv. Akad. Nauk SSSR Ser. Math. 41 (1977), 235-252 (Math. USSR-Izvestia 11 (1977), 221-238). MR 0472792 (57:12482)
- 26.
- A. A. Suslin and L. N. Vaserstein, Serre's problem on projective modules over polynomial rings and algebraic K-theory, Izv. Akad. Nauk SSSR Ser. Math. 40 (1976), 993-1054 (Math. USSR-Izvestia 10 (1976), 937-1001). MR 0447245 (56:5560)
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Additional Information:
Reviewer(s):
Richard
G.
Swan
Affiliation:
University of Chicago
Email:
swan@math.uchicago.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
45
(2008),
451-457.
MSC
(2000):
Primary 13--02, 13B25, 13C10, 13D15
DOI:
10.1090/S0273-0979-08-01171-3
PII:
S 0273-0979(08)01171-3
Posted:
January 7, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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