ةtale descent for real number fields

In this paper we verify the strong Quillen–Lichtenbaum conjecture for integers in real number fields at the prime two. That is, we prove that the Dwyer–Friedlander map from mod 2 algebraic K-theory to mod 2 étale topological K-theory is a weak equivalence on zero-connected covers for two integers in real number fields. The proof is given by comparing two explicit calculations.