Hermitian K-theory of the integers

Details Hermitian K-theory of the integers Hermitian K-theory of the integers

2005-09-18

arxiv.org/abs/math/0509404v1

Amer. Journal Math. 127 (2005) 785-823

Mathematics

K-Theory and Homology

36 pages ; see also http://www.math.jussieu.fr/~karoubi/ and http://www.math.nus.edu.sg/~matberic/

Scientific paper

The 2-primary torsion of the higher algebraic K-theory of the integers has been computed by Rognes and Weibel. In this paper we prove analogous results for the Hermitian K-theory of the integers with 2 inverted (denoted by Z'). We also prove in this case the analog of the Lichtenbaum conjecture for the hermitian K-theory of Z' : the homotopy fixed point set of a suitable Z/2 action on the classifying space of the algebraic K-theory of Z' is the hermitian K-theory of Z' after 2-adic completion.

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