The 2-torsion in the K-theory of the integers

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)615-620
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume324
Issue number6
DOIs
StatePublished - Jan 1 1997

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'The 2-torsion in the K-theory of the integers'. Together they form a unique fingerprint.

Cite this