On the relation between 2 and infty in Galois cohomology of number fields

Abstract

We remove the assumption "let p be odd or k totally imaginary" from several well-known theorems in Galois cohomology of number fields. For example, we show that the Galois group of the maximal extension of a number field k which is unramified outside 2 has a finite cohomological 2-dimension (also if k has real places). (The dvi-file requires the xypic-package)