A localisation principle for quadratic spaces over Laurent extensions

Parimala, Raman; Sinclair, Parvin

doi:10.1090/S0002-9939-1983-0712622-9

A localisation principle for quadratic spaces over Laurent extensions
HTML articles powered by AMS MathViewer

by Raman Parimala and Parvin Sinclair PDF

Proc. Amer. Math. Soc. 89 (1983), 202-204 Request permission

Abstract:

We prove here that the localisation principle holds for anisotropic quadratic spaces over $R[T,{T^{ - 1}}]$, where $R$ is an integral domain in which 2 is invertible. We also give an example of an isotropic quadratic space over $R[T,{T^{ - 1}}]$ for which the localisation principle does not hold.

References

Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
M.-A. Knus, Raman Parimala, and R. Sridharan, Nonfree projective modules over $\textbf {H}[X,\,Y]$ and stable bundles over $P_{2}(\textbf {C})$, Invent. Math. 65 (1981/82), no. 1, 13–27. MR 636877, DOI 10.1007/BF01389292
T. Y. Lam, Series summation of stably free modules, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 37–46. MR 396678, DOI 10.1093/qmath/27.1.37
Raman Parimala and R. Sridharan, A local global principle for quadratic forms over polynomial rings, J. Algebra 74 (1982), no. 1, 264–269. MR 644232, DOI 10.1016/0021-8693(82)90019-9
Richard G. Swan, Projective modules over Laurent polynomial rings, Trans. Amer. Math. Soc. 237 (1978), 111–120. MR 469906, DOI 10.1090/S0002-9947-1978-0469906-4