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The Lichtenbaum-Quillen Conjecture for Fields

Published online by Cambridge University Press:  20 November 2018

J. F. Jardine
J. F. Jardine*
Affiliation:
Mathematics Department University of Western Ontario London, Ontario N6A 5B7
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I want to say immediately that, despite the authoritative-sounding title, I am not claiming a proof of anything like the Lichtenbaum-Quillen conjecture. My intent here is only to explain the conjecture in various special cases, but maybe from an idiosyncratic point of view.

This paper is based on the text of the Coxeter-James Lecture given at the Winter Meeting of the Canadian Mathematical Society at Montreal in December, 1992.1 would like to thank the Society for awarding me the honour of giving this talk.

Keywords

19E20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 4 , 01 December 1993 , pp. 426 - 441
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Bass, H., Heller, A. and Swan, R. G., The Whitehead group of a polynomial extension, Inst. Hautes Etudes Sci. Publ. Math. 22(1964), 61–79.Google Scholar
2. Browder, W., Algebraic K-theory with coefficients ℤ/p, Springer Lecture Notes in Math. 657(1978), 40–84.Google Scholar
3. Dwyer, W. G. and Friedlander, E. M., Algebraic and étale K-theory, Trans. AMS 292( 1985), 247–280.Google Scholar
4. Friedlander, E. M., Etale K-theory I: Connections with Etale Cohomology and Algebraic Vector Bundles, InventionesMath. 60(1980), 105–134.Google Scholar
5. Gabber, O., K-theory ofHenselian local rings andHenselianpairs, Contemporary Math. 126(1992), 59–70.Google Scholar
6. Gersten, S. M., Higher K-theory of rings, Springer Lecture Notes in Math. 341(1973), 3–42.Google Scholar
7. Harris, B., Bott periodicity via simplicial spaces, J. Algebra 62(1980), 450–454.Google Scholar
8. Jardine, J. F., Simplicial objects in a Grothendieck topos, Contemporary Math. (I) 55(1986), 193–239.Google Scholar
9. Jardine, J. F., Simplicial pre sheaves, J. Pure Applied Algebra 47(1987), 35–87.Google Scholar
10. Jardine, J. F., Stable homotopy theory of simplicial pre sheaves, Can. J. Math. 39(1987), 733–747.Google Scholar
11. Joyal, A., Letter to A. Grothendieck 11/4/84.Google Scholar
12. Kahn, B., Some Conjectures on the Algebraic K-theory of Fields, I: K-theory with Coefficients and Etale K-theory, In: Algebraic A'-theory: Connections with Geometry and Topology, NATO ASI Series C 279, Kluwer, Dordrecht, 1989,117–176.Google Scholar
13. Kahn, B., On the Lichtenbaum-Quillen conjecture. In: Algebraic A'-theory and Algebraic Topology, NATO ASI Series C, 1993, to appear.Google Scholar
14. Levine, M., The indecomposable K3 of fields, Ann. scient. Ec. Norm. Sup. 22(1989), 255–344.Google Scholar
15. Merkurjev, A. S. and Suslin, A. A., K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR Izvestiya 21(1983), 307–340.Google Scholar
16. Merkurjev, A. S. and Suslin, A. A., On the norm residue homomorphism of degree 3, Math. USSR Izvestiya 36(1991 ), 349–367.Google Scholar
17. Milnor, J., Introduction to Algebraic K-theory, Annals of Math. Studies 72, Princeton University Press, Princeton, 1971.Google Scholar
18. Quillen, D., On the cohomology and K-theory of the general linear groups over a finite field, Annals of Math. 96(1972), 552–586.Google Scholar
19. Quillen, D., Higher algebraic K-theory I, Springer Lecture Notes in Math. 341(1973), 85–147.Google Scholar
20. Suslin, A. A., On the K-theory of algebraically closed fields, Invent. Math. 73(1983), 241–245. 21 , On the K-theory of local fields, J. Pure Applied Algebra 34(1984), 301–318.Google Scholar
22. Thomason, R. W., Algebraic K-theory and étale cohomology, Ann. Scient. Ec. Norm. Sup. 18(1985), 437– 552.Google Scholar