Abstract
REMARK . The requirement that / be an odd prime can be dropped if K is totally imaginary. The groups on the right of (1.1) are continuous /-adic etale cohomology groups. Recall that Z//(l) denotes the sheaf of ^th roots of unity, Z/P(i) = (Z//(l))®, and Z,(0 = Hmv Z/l (i). D. Quillen has conjectured the existence of isomorphisms of type (1.1). B. Harris and G. Segal [4] have shown that (1.1) is surjective on torsion if k = 1; C. Soule [6] in many cases proved surjectivity for k = 2 with i < I. The surjectivity of (1.1) together with A. Borel's computation of K^(0) ® Q [1] gives a new proof of the existence [7] of isomorphisms
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