Two-primary algebraic \(K\)-theory of two-regular number fields (Q1968577)

In the paper ``Two-primary algebraic \(K\)-theory of rings of integers in number fields'' [J. Am. Math. Soc. 13, No. 1, 1-54 (2000; Zbl 0934.19001)], \textit{J. Rognes} and \textit{C. Weibel} expressed the \(2\)-primary algebraic \(K\)-groups of rings of integers in arbitrary number fields in terms of the étale cohomology groups of the number ring, using Voevodsky's proof of the Milnor conjecture and the Bloch-Lichtenbaum spectral sequence. Based upon these results, the authors of the paper under review explicitly calculate all the \(2\)-primary higher algebraic \(K\)-groups of the rings of integers of all \(2\)-regular quadratic number fields, cyclotomic number fields, or maximal real subfields of such. Here \(2\)-regular means that \((2)\) does not split in the number field, and its narrow Picard group is of odd order.