On 2-adic Cyclotomic Elements in K-theory and Étale Cohomology of the Ring of Integers Original Research Article

In this paper we define 2-adic cyclotomic elements in K-theory and étale cohomology of the integers. We construct a comparison map which sends the 2-adic elements in K-theory onto 2-adic elements in cohomology. Using calculation of 2-adic K-theory of the integers due to Voevodsky, Rognes and Weibel, we show which part of the group K2n−1(image)circle times operatorimagelogical and2 for n odd, is described by the 2-adic cyclotomic elements. We compute explicitly some of the product maps in K-theory of image at the prime 2.