Overview

In various contexts of topology, algebraic geometry, and algebra (e.g. group representations), one meets the following situation. One has two contravariant functors K and A from a certain category to the category of rings, and a natural transformation p:K--+A of contravariant functors. The Chern character being the central exam- ple, we call the homomorphisms Px: K(X)--+ A(X) characters. Given f: X--+ Y, we denote the pull-back homomorphisms by and fA: A(Y)--+ A(X). As functors to abelian groups, K and A may also be covariant, with push-forward homomorphisms and fA: A( X)--+ A(Y). Usually these maps do not commute with the character, but there is an element r f E A(X) such that the following diagram is commutative: K(X)~A(X) fK j J~A K( Y) ------p;-+ A( Y) The map in the top line is p x multiplied by r f. When such commutativity holds, we say that Riemann-Roch holds for f. This type of formulation was first given by Grothendieck, extending the work of Hirzebruch to such a relative, functorial setting. Since then viii INTRODUCTION several other theorems of this Riemann-Roch type have appeared. Un- derlying most of these there is a basic structure having to do only with elementary algebra, independent of the geometry. One purpose of this monograph is to describe this algebra independently of any context, so that it can serve axiomatically as the need arises.

Full Product Details

Author:   William Fulton ,  Serge Lang
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1985 ed.
Volume:   277
Dimensions:   Width: 15.60cm , Height: 1.50cm , Length: 23.40cm
Weight:   1.080kg
ISBN:  

9780387960869

ISBN 10:   0387960864
Pages:   206
Publication Date:   15 August 1985
Audience:   General/trade ,  College/higher education ,  General ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

I ?-Rings and Chern Classes.- II Riemann-Roch Formalism.- III Grothendieck Filtration and Graded K.- IV Local Complete Intersections.- V The K-functor in Algebraic Geometry.- VI An Intersection Formula. Variations and Generalizations.- References.- Index of Notations.

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