Gersten complex

Summary

The Gersten complex of a scheme $X$ in degree $n$ is a complex built from the points of $X$, grouped by codimension. Its terms are sums of algebraic K-groups of the residue fields of these points. Its differentials come from Quillen's localization sequence. For smooth varieties over a field it gives a flasque resolution of the K-theory sheaf, which leads to Bloch's formula.