Algèbre homologique/Homological Algebra The 2-torsion in the K-theory of the Integers

  title={Algèbre homologique/Homological Algebra The 2-torsion in the K-theory of the Integers},
  author={Charles Weibel}
  • Charles Weibel
Using recent results of Voevodsky, Suslin-Voevodsky and BlochLichtenbaum, we completely determine the 2-torsion subgroups of the K-theory of the integers Z. The result is periodic of order 8, and there are no 2-torsion elements except those which have been 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 ζ(1 − 2n) is twice the 2… CONTINUE READING
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