Riemann-Roch algebra / William Fulton, Serge Lang

The Riemann-Roch theorem has played a major role in the development of the algebraic geometry. During the fiftieth Hirzebruch proved it in full generality for complex projective manifolds. Soon after, Grothendieck has generalized it, in a functorial setting, to relative context of maps and introduced for that purpose the K-group. All these ideas were afterwards extended and played a central role in several branches of mathematics. The aim of the book is the study of pure algebraic formalism underlying most of the theorems of Grothendieck-Riemann-Roch-type, independently of the geometrical context. This kind of algebra is called here Riemann-Roch algebra. Then, this formalism is applied to give a complete elementary proof of GRR-theorem for local complete intersection morphism of schemes. Several other related topics are presented. The book is self-contained, requiring from the reader very few facts of general algebra, commutative algebra and algebraic geometry. (Zentralblatt)