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Proceedings of the American Mathematical Society

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On the localisation sequence in $ K$-theory

Author: Victor Snaith
Journal: Proc. Amer. Math. Soc. 79 (1980), 359-364
MSC: Primary 18F25; Secondary 12B22
MathSciNet review: 567972
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Abstract: A description of the boundary map in Quillen's localisation sequence is given in terms of classifying spaces of categories. Using this description the low dimensional part of the localisation sequence for a Dedekind domain is shown to coincide with the algebraically defined Bass-Tate sequence.

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  • [G-Q] Daniel Grayson, Higher algebraic 𝐾-theory. II (after Daniel Quillen), Algebraic 𝐾-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976), Springer, Berlin, 1976, pp. 217–240. Lecture Notes in Math., Vol. 551. MR 0574096
  • [L] Jean-Louis Loday, 𝐾-théorie algébrique et représentations de groupes, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 3, 309–377 (French). MR 0447373
  • [M] John Milnor, Introduction to algebraic 𝐾-theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. Annals of Mathematics Studies, No. 72. MR 0349811
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Keywords: Algebraic K-theory, category, Dedekind domain, localisation, tame symbol, valuation
Article copyright: © Copyright 1980 American Mathematical Society