Motivic cohomology

Summary

Motivic cohomology is a cohomology theory for algebraic varieties, with groups $H^p(X, \Z(q))$ indexed by two integers. It contains the Chow groups of algebraic cycles and the Milnor K-groups of fields as special cases. It plays for algebraic K-theory the role that ordinary cohomology plays for topological K-theory. Its comparison with étale cohomology, with finite coefficients, is the content of the norm residue isomorphism theorem.