For rings with a large number of units the authors prove a strengthened theoremon homological stabilization: the homomorphism Hk(GLn(A)) 薔 Hk(GL(A)) is surjective for n 蠅 k + sr A 舑 1 and bijective for n 蠅 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)) 薔 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.
|Original language||English (US)|
|Number of pages||25|
|Journal||Mathematics of the USSR - Izvestija|
|State||Published - Feb 28 1990|
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