Download Algebraic K-Theory and Algebraic Topology by Robert Boltje, G.-Martin Cram, V. P. Snaith (auth.), P. G. PDF

By Robert Boltje, G.-Martin Cram, V. P. Snaith (auth.), P. G. Goerss, J. F. Jardine (eds.)

A NATO complicated examine Institute entitled "Algebraic K-theory and Algebraic Topology" used to be held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December sixteen of 1991. This ebook is the quantity of court cases for this assembly. The papers that seem listed below are consultant of many of the lectures that got on the convention, and hence current a "snapshot" of the kingdom ofthe K-theoretic artwork on the finish of 1991. The underlying goal of the assembly used to be to debate fresh paintings relating to the Lichtenbaum-Quillen advanced of conjectures, fro~ either the algebraic and topological issues of view. The papers during this quantity care for a number of themes, together with motivic cohomology theories, cyclic homology, intersection homology, better category box concept, and the previous telescope conjecture. This assembly was once together funded by way of delivers from NATO and the nationwide technology Foun­ dation within the usa. i want to take this chance to thank those businesses for his or her help. i'd additionally wish to thank the opposite contributors of the organizing com­ mittee, particularly Paul Goerss, Bruno Kahn and Chuck Weibel, for his or her assist in making the convention winning. This used to be the second one NATO complicated examine Institute to be held during this venue; the 1st used to be in 1987. The good fortune of either meetings owes a lot to the professionalism and helpfulness of the management and employees of castle Lake Louise.

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M. R. Stein and R. K. Dennis, Contemporary Mathematics 83, Amer. Math. , Providence, RI, 1989, 101-131. S. Milne : Etale cohomology; Princeton Mathematical Series University Press. -C. Rota: On the foundations of combinatorial theory I. Theory of Mobius functions; Z. Wahrsch verw. Gebiete 2 (1964) 340-368. (10] J-P. Serre : Linear Representations of Finite Groups; (1977) Springer-Verlag. Grad. Texts in Math. # 42 (11] Jean-Pierre Serre : Corps locaux; Hermann, Paris (1962). [12] J-P. Serre : Sur la rationalite des representations d'Artin; Annals of Math.

1. - Let X be a smooth, projective, geometrically integral variety over a finite field F, dim(X) = d, and let l "/:- char( F). Then the following properties hold: a) Hd- 1 (X,K:a) 0 Q,jZ1 is zero. d(Q_,jZi(d))) isfinite. The map Hd- 1 (X, 1id(Q_,jZI(d)))---+ CHd(X)I-tors is an isomorphism. d(Q_,jZI(d)))---+ Hi1d- 1 (X,Q,jZ1(d)) is an isomorphism. d+ 1 (Q,jZi(d)))) ....... d(Q_,jZi(d))) van- ishes. d+l(Q1/Z1(d))) is surjective. d+ 1(QI/ZI(d))) is finite. Proof: Note that the divisible group Hd- 1 (X,K:d) 0 Q,jZ1 is zero if and only if it is finite.

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