Riemann-Roch Algebra (Grundlehren der mathematischen Wissenschaften) (v. 277)

Shipped from UK, please allow 10 to 21 business days for arrival. Riemann-Roch algebra, hardcover, 203pp. ill. Includes index. p. [197]-198. Good copy, previous owners name inside front end-paper. 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 Front Matter....Pages i-x λ -Rings and Chern Classes....Pages 1-25 Riemann-Roch Formalism....Pages 26-46 Grothendieck Filtration and Graded K ....Pages 47-65 Local Complete Intersections....Pages 66-99 The K -Functor in Algebraic Geometry....Pages 100-150 An Intersection Formula. Variations and Generalizations....Pages 151-196 Back Matter....Pages 197-205 William Fulton, Serge Lang. Includes Indexes. Bibliography: P. [197]-198.