By Barry Dayton, Charles Weibel (auth.), J. F. Jardine, V. P. Snaith (eds.)

A NATO complex learn Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was once held on the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December eleven of 1987. This assembly used to be together supported via NATO and the ordinary Sciences and Engineering learn Council of Canada, and was once subsidized partly by means of the Canadian Mathematical Society. This booklet is the amount of complaints for that assembly. Algebraic K-theory is largely the examine of homotopy invariants coming up from jewelry and their linked matrix teams. extra importantly possibly, the topic has develop into principal to the examine of the connection among Topology, Algebraic Geometry and quantity thought. It attracts on all of those fields as a subject matter in its personal correct, however it serves in addition to an efficient translator for the applying of thoughts from one box in one other. The papers during this quantity are consultant of the present country of the topic. they're, for the main half, learn papers that are essentially of curiosity to researchers within the box and to these intending to be such. there's a part on difficulties during this quantity which will be of specific curiosity to scholars; it features a dialogue of the issues from Gersten's recognized record of 1973, in addition to a brief record of latest problems.

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Benjamin. New York. 1968. : 'The Picard group of a reduced G-algebra', to appear in J. Pure Applied Algebra. [FL] Fulton, W. , Springer. 1985. : Cohomologie non abelienne, Grundlehren der Math, Springer, 1971. , 1977. , Springer, 1966. : Etale Cohomology, Princeton U. Press, Princeton, 1980. : Introduction to Algebraic K-theory, Ann. of Math. Studies 72, Princeton U. Press, Princeton, 1971. [SGA6] Berthelot, P. : Theorie des intersections et theoreme de Riemann-Roch (SGA6) , Lecture Notes in Math.

For any commutative. A+). A= R mAl m ... A+}. be a commutative graded ring. are naturally continuous W(R)-submodules In particular. 4 Corollary: of 23 R contains the rational numbers, is naturally an R-module. 3 does not apply, but arguments of [Vorst] do). APPENDIX. PATCHING VECfOR BUNDLES It is well known that a rank n vector bundle P on a scheme be obtained by patching free 0U-modules on some open cover X via matrices guy € GLn(U n V} on each U n V. this data, the determinant line bundle 0u together via the units SL (U n n V), det(guv}, the line bundle Anp Anp If P ~ X may = {U} of is given by is formed by patching the so if each is trivial.

One can show that the induced map from cycles to Deligne cohomology is compatible with rational equivalence, and therefore gives a map Notice that if H2p (X,Z} , CHP(X)h = d~ is an algebraic cycle which is homologous to zero in then ,feZ) E JP(X). JP(X) . to as follows. ) maps from an integral current (such as integration over a chain ~ Z).