Algebraic K-theory

Summary

Algebraic K-theory attaches to a ring $R$ a sequence of abelian groups $K_n(R)$. The group $K_0(R)$ is the Grothendieck group of finitely generated projective modules, and $K_1(R)$ is the abelianization of the infinite general linear group. Daniel Quillen defined the higher groups by homotopy theory, for instance through the plus construction. The groups encode deep arithmetic information, such as class groups, units and special values of zeta functions.