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 complicated research 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 was once together supported by way of NATO and the average Sciences and Engineering learn Council of Canada, and was once subsidized partly by means of the Canadian Mathematical Society. This e-book is the amount of complaints for that assembly. Algebraic K-theory is basically the examine of homotopy invariants bobbing up from jewelry and their linked matrix teams. extra importantly possibly, the topic has turn into vital to the learn of the connection among Topology, Algebraic Geometry and quantity concept. 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 ideas from one box in one other. The papers during this quantity are consultant of the present nation of the topic. they're, for the main half, learn papers that are basically of curiosity to researchers within the box and to these desiring to be such. there's a part on difficulties during this quantity which might be of specific curiosity to scholars; it encompasses a dialogue of the issues from Gersten's recognized checklist of 1973, in addition to a quick checklist of latest problems.

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V) is a bundle * (f E,f*v). Since Chern classes are integral and hence real. and the exterior derivative is a real operator. we can take the real part of the characteristic classes described above. ffiIZ) for p We obtain classes in A cp(E,v)rn ~ 0 which are characterized by axioms similar to those above except that i) is replaced by: i)rn If E is a line bundle and to the zero section of E. v) = (div(s). Re{2v~ }). rn». represent the Chern classes in is already real. for example if Hermitian metric on E.

Algebraic K-theory. 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.

G) is a subset of (For more details. see [Hirz. 1J. [Milne. 122]. [Gir. ) For example. the patching data described above for the vector bundle P forms a l-cocyle for ~ with values in 1-1 correspondence between the set rank n vector bundles on X. SL) n of "rank n [St] [Weil]. n If vector bundles on X with structure group P € SP (X). then the patching maps n above. this implies that Proposition: Let An{p) the pointed set SL (U n n V). The group A* and the orbit set SP (X). n to the pointed set of all rank guy for As we observed = OX' X be a scheme.

### 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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