The Merkuriev–Suslin theorem for any semi-local ring

We introduce here a method which uses étale neighborhoods to extend results from smooth semi-local rings to arbitrary semi-local rings A by passing to the henselization of a smooth presentation of A. The technique is used to show that étale cohomology of A agrees with Galois cohomology, to show that the Merkuriev–Suslin theorem holds for A, and to describe torsion in K2(A).