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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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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  • [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 (56 #5686)
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  • [Q] Daniel Quillen, Higher algebraic 𝐾-theory. I, Algebraic 𝐾-theory, I: Higher 𝐾-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, pp. 85–147. Lecture Notes in Math., Vol. 341. MR 0338129 (49 #2895)

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Additional Information

PII: S 0002-9939(1980)0567972-3
Keywords: Algebraic K-theory, category, Dedekind domain, localisation, tame symbol, valuation
Article copyright: © Copyright 1980 American Mathematical Society