Algebraic K-theory of schemes

Summary

The algebraic K-theory of a scheme $X$ is a sequence of abelian groups $K_0(X), K_1(X), \ldots$ built from the category of vector bundles on $X$. The group $K_0(X)$ is the Grothendieck group of vector bundles, and the higher groups are defined by Quillen's Q-construction. K-theory is the setting of the Grothendieck–Riemann–Roch theorem. It is linked to Chow groups by the Chern character and to motivic cohomology by spectral sequences.