Summary
We give several proofs that a stably free module of even rank need not be self-dual.
With best wishes to Parimala on the 21st of November
2010 Mathematics subject classification. Primary: 13C10, 19A13. Secondary: 14C25, 19B14, 19L10, 55Q05, 55R25.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Bass, Modules which support nonsingular forms. J. Algebra 13 (1969), 246–252.
P. Berthelot, A. Grothendieck, L. Illusie, et al., Théorie des Intersections et Théorème de Riemann–Roch, SGA6, 1966/1967, Lecture notes in Math. 225, Springer-Verlag, Berlin, 1971.
R. Bott, The space of loops on a Lie group, Mich. Math. J. 5 (1958), 35–61.
R. Bott-, The stable homotopy of the classical groups, Ann. Math. 70 (1959), 313–337.
R. Fossum, H. B. Foxby, and B. Iversen, A characteristic class in algebraic K-theory, Aarhus University Preprint No. 29, 1978/79.
A. Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1958), 137–154.
D. Husemoller, Fibre bundles, Third edition, Graduate Texts in Mathematics 20, Springer-Verlag, New York, 1994. ISBN: 0-387-94087-1.
T. Y. Lam, Serre’s Problem on Projective Modules, Monographs in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York, 2006.
M. Roitman, On stably extended projective modules over polynomial rings, Proc. Amer. Math. Soc. 97 (1986), 585–589.
N. Steenrod, The Topology of Fibre Bundles. Princeton Mathematical Series, vol. 14. Princeton University Press, Princeton, N.J., 1951.
A. A. Suslin, Stably free modules. (Russian) Math. Sbornik (N.S.) 102 (144), No. 4, 537–550, 632, 1977; English translation in Math. USSR Sbornik Vol 31, 479–491, 1977.
A. A. Suslin-, Mennicke symbols and their applications in the K-theory of fields. Algebraic K-theory, Part I (Oberwolfach, 1980), pp. 334–356, Lecture Notes in Math. 966, Springer, Berlin-New York, 1982.
A. A. Suslin--, K-theory and K-cohomology of certain group varieties. Algebraic K-theory, 53–74, Adv. Soviet Math. 4, American Mathematical Socity, Providence, RI, 1991.
R. G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc. 105(1962), 264–277.
R. G. Swan-, Vector Bundles, Projective Modules and the K-theory of Spheres, 432–522, Ch. XVIII, Algebraic Topology and Algebraic K-theory, ed. W. Browder, Annals of Mathematics Studies 113, Princeton University Press, Princeton, NJ, 1987.
R. G. Swan--, Some stably free modules which are not self dual. http://www.math.uchicago.edu/\~{}swan/stablyfree.pdf
R. G. Swan---, On a theorem of Mohan Kumar and Nori, http://www.math.uchicago.edu/\~{}swan/MKN.pdf
R. G. Swan, J. Towber, A class of projective modules which are nearly free, J. Algebra 36 (1975), 427–434.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer New York
About this chapter
Cite this chapter
Nori, M.V., Rao, R.A., Swan, R.G. (2010). Non-self-dual Stably Free Modules. In: Colliot-Thélène, JL., Garibaldi, S., Sujatha, R., Suresh, V. (eds) Quadratic Forms, Linear Algebraic Groups, and Cohomology. Developments in Mathematics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6211-9_20
Download citation
DOI: https://doi.org/10.1007/978-1-4419-6211-9_20
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-6210-2
Online ISBN: 978-1-4419-6211-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)