Homology of the Full Linear Group Over a Local Ring, and Milnor'sk-Theory

For rings with a large number of units the authors prove a strengthened theorem on homological stabilization: the homomorphism Hk(GLn(A)) → Hk(GL(A)) is surjective for n ≥ k + sr A – 1 and bijective for n ≥ k + sr A. If A is a local ring with an infinite residue field, then this result admits further refinement: the homomorphism Hn(GLn(A)) → Hn(GL(A)) is bijective and the factor group Hn(GL(A)) / Hn(GLn -1(A)) is canonically isomorphic to Milnor's nth K-group of the ring A. The results are applied to compute the Chow groups of algebraic varieties. Bibliography: 16 titles.