Using recent results of Voevodsky, Suslin-Voevodsky and Bloch-Lichtenbaum, we completely determine the 2-torsion subgroups of the K-theory of the integers ℤ. The result is periodic with period 8, and there are no 2-torsion elements except those known for over 20 years. There is no 2-torsion except for the ℤ/2 summands in degrees 8n+1 and 8n + 2, the ℤ/16 in degrees 8n + 3 and the image of the J-homomorphism in degrees 8n + 7. In particular, the 2-part of σ(1 - 2n) is twice the 2-part of the ratio |K4n-2(ℤ)|/|K4n-1(ℤ)| for all n > 0. This corrects a conjecture of Lichtenbaum.
|Original language||English (US)|
|Number of pages||6|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|State||Published - Jan 1 1997|
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