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

ISBN-10: 9400923996

ISBN-13: 9789400923997

ISBN-10: 9401075808

ISBN-13: 9789401075800

A NATO complex research Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" used to be held on the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December eleven of 1987. This assembly was once together supported by way of NATO and the common Sciences and Engineering study Council of Canada, and was once backed partially by way of the Canadian Mathematical Society. This ebook is the quantity of complaints for that assembly. Algebraic K-theory is basically the research of homotopy invariants bobbing up from earrings and their linked matrix teams. extra importantly possibly, the topic has develop into principal to the research of the connection among Topology, Algebraic Geometry and quantity conception. It attracts on all of those fields as a subject matter in its personal correct, however it serves in addition to a good translator for the appliance of options from one box in one other. The papers during this quantity are consultant of the present kingdom of the topic. they're, for the main half, study papers that are essentially of curiosity to researchers within the box and to these meaning 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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**Additional info for Algebraic K-Theory: Connections with Geometry and Topology**

**Sample text**

16 of [4]. 7. 6 can be used to 'compute' the analytic torsion of a Hermitian vector bundle on an arithmetic variety. nonsingular projective variety over Hermitian vector bundle over = det(R~*(E» A(E) on X. Spec(~). Let us suppose that Spec(~). E»<-I)i i~O IQ A(E). II II) X is a XlSpec{~) • Spec{lQ) X. e. on the then we can define a metric on the Quillen metric. which is the product of the metric induced A(E) by the L2 metric on the space(s) with coefficients in E. of harmonic forms on Xro and the Ray-Singer analytic torsion ([24]).

Ffi) currents of the form dCg is a d-closed. exact current. c such that dd g = oZ. ffi). ffi) then Hence there is unique up to adding h a harmonic form. ffi». rn)/~;(X». 4. The range of the map intermediate Jacobian of tp is isomorphic to the p-th (Griffiths) X: which is itself the range of the Griffiths' Abel-Jacobi homomorphism a description of which may be found in [IS]. In the next paragraph we eP . First we shall give an alternative shall identify ~p description of eP . C) be the complex of complex valued currents on X.

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. 225, Springer-Verlag, 1971. : The Topology of Fibre Bundles, Princeton U. Press, Princeton, 1951. T. Algebra 67, 210-229, 1980. : 'Descent for the K-theory of polynomial rings', Math. Zeit. 191, 405-415, 1986. : 'Localization of the K-theory of polynomial extensions', Math.

### Algebraic K-Theory: Connections with Geometry and Topology by Barry Dayton, Charles Weibel (auth.), J. F. Jardine, V. P. Snaith (eds.)

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