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

✍ Scribed by Dominique Arlettaz; Grzegorz Banaszak; Wojciech Gajda


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
255 KB
Volume
82
Category
Article
ISSN
0022-314X

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✦ Synopsis


In this paper we define 2-adic cyclotomic elements in K-theory and e tale 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 K 2n&1 (Z) Z 7 2 for n odd, is described by the 2-adic cyclotomic elements. We compute explicitly some of the product maps in K-theory of Z at the prime 2.


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