Opérations en K-théorie algébrique. (French) Zbl 0575.14015

Soulé, Christophe

Can. J. Math. 37, 488-550 (1985).

Grothendieck originally defined the group \(K_ 0(X)\) for a scheme X and developed its structure as a \(\lambda\)-ring in order to extend the Riemann-Roch theorem to an arbitrary projective morphism. When X is affine the higher K-groups, \(K_ i(A)\) of Quillen, had been shown to possess a structure of a graded \(\lambda\)-ring [H. Hiller, J. Pure Appl. Algebra 20, 241-266 (1981; Zbl 0471.18007), C. Kratzer, Enseign. Math., II. Ser. 26, 141-154 (1980; Zbl 0444.18009)].
The author extends this to the higher K-groups, \(K_ i(X)\), of a scheme X. He then pursues the Grothendieck programme, studying the \(\lambda\)- ring \(K_*(X)\) and proving such results as the Riemann-Roch theorem (without denominators).

Reviewer: V.P.Snaith

MSC:

14C35	Applications of methods of algebraic \(K\)-theory in algebraic geometry
18F30	Grothendieck groups (category-theoretic aspects)
14C40	Riemann-Roch theorems
18F25	Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)

Keywords:

Riemann-Roch theorem

Citations:

Zbl 0471.18007; Zbl 0444.18009