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l-adic and Z/l∞-algebraic and topological K-theory

Published online by Cambridge University Press:  20 January 2009

Victor Snaith
Victor Snaith
Affiliation:
Department of MathematicsUniversity Of Western OntarioLondon, Ontario N6A 5B7, Canada
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Let l be an odd prime and let A be a commutative ring containing 1/l. Let K*(A;Z/lv) denote the mod lv algebraic K-theory of A [3]. As explained in [4] there exists a “Bott element” βv∈K21v–1(l–1)(Z[1/l];Z/lv) and, using the K-theory product we may, following [16, Part IV], form

which is defined as the direct limit of iterated multiplication by βv. There is a canonical localisation map

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 1 , February 1985 , pp. 73 - 90
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

1.Adams, J. F., On the groups J(X), IV, Topology 5 (1966), 21–71.CrossRefGoogle Scholar
2.Adams, J. F., Stable Homotopy and Generalised Homology (Chicago Lecture Notes in Mathematics, 1974).Google Scholar
3.Browder, W., Algebraic K-theory with Coefficients Z/p (Lecture Notes in Mathematics No. 654, Springer-Verlag, 1978), 40–84.Google Scholar
4.Dwyer, W. G., Friedlander, E. M., Snaith, V. P. and Thomason, R. W., Algebraic K-theory eventually surjects onto topological K-theory, Inventiones Math. 66 (1982), 481–491.Google Scholar
5.Grayson, D. (after D. G. Quillen), Higher Algebraic K-theory II (Lecture Notes in Mathematics, No. 551, 0000, Springer-Verlag), 217–240.Google Scholar
6.Hodgkin, L., Dyer-Lashof Operations in K-theory (London Math. Soc. Lecture Notes No. 11, 1974), 27–33.CrossRefGoogle Scholar
7.Hodgkin, L. and Snaith, V. P., The K-theory of some more well-known spaces, Illinois J. Math (2) 22 (1978), 270–278.Google Scholar
8.Loday, J-L., K-théorie algébrique et représentations de groupes, Ann. Sci. EC. Norm. Sup 4e serie 9 (1976), 309–377.Google Scholar
9.Madsen, I., Higher torsion in SG and BSG, Math. Zeit. 143 (1975), 55–80.CrossRefGoogle Scholar
10.McClure, J. E., Dyer-Lashof operations in K-theory, Bull. Amer. Math. Soc. (1) 8 (1983), 67–72.Google Scholar
11.McClure, J. E. and Snaith, V. P., On the K-theory of the extended power construction, Math. Proc. Cambs. Philos. Soc. (2) 92 (1982), 263–274.Google Scholar
12.May, J. P., Geometry of Iterated Loopspaces (Lecture Notes in Mathematics No. 271, 0000, Springer-Verlag).Google Scholar
13.May, J. P. (with contributions by Frank Quinn, Nigel Ray and Jørgen Tornehave), E∞-ring Spaces and E∞-ring Spectra (Lecture Notes in Mathematics No. 577, 0000, Springer-Verlag).CrossRefGoogle Scholar
14.Snaith, V. P., Dyer—Lashof Operations in K-theory (Lecture Notes in Mathematics No. 496, 0000, Springer-Verlag), 100–299.Google Scholar
15.Snaith, V. P., Unitary K-homology and the Lichtenbaum-Quillen conjecture on the algebraic K-theory of schemes, Algebraic Top. Conf., Aarhus 1982 (Lecture Notes in Mathematics No. 1051, 0000, Springer-Verlag), 128–155.Google Scholar
16.Snaith, V. P., Algebraic Cobordism and K-theory (Mem. A. M. Soc. No. 221, 1979).Google Scholar
17.Thomason, R. W., Algebraic K-theory and étale cohomology (preprint M.I.T., 1981).Google Scholar
18.Thomason, R. W., The Lichtenbaum–Quillen conjecture for K/l*[l/β], Proc. Current Trends in Algebraic Topology (Can. Math. Soc. Conf. Proc. Series No. 2, Part 1, 1982), 117–140.Google Scholar
19.Weibel, C. A., Mayer–Vietoris Sequences (Lecture Notes in Mathematics No. 966, 0000, Springer-Verlag), 390–407.Google Scholar