Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [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
  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 18F25, 12B22

Retrieve articles in all journals with MSC: 18F25, 12B22


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0567972-3
Keywords: Algebraic K-theory, category, Dedekind domain, localisation, tame symbol, valuation
Article copyright: © Copyright 1980 American Mathematical Society