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

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
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